Varys knows Arya's whereabouts.

[Manderly's Rat Cook]

I believe Varys knows a lot more about Arya's whereabouts than we're led to believe. 

Let me explain why. 

So Varys has his little birds spying on Ned in the tower of the hand,  probably 24/7.

Then there comes the day that Arya goes missing. Varys must've known that. Later Arya shows up outside the castle gates,  and since we know that Varys has spies in the city gates,  who report to him who enters and leaves the city (which we learn in the Tyrion chapter where Varys pays his first visit to Shae) we can also be certain that he knows who enters and leaves the castle. 

If I were Varys I would want to know how Stark's daughter left the castle,  without being noticed,  so if he didn't already have eyes on Ned, he definitely would have by now.

Ned doesn't understand the confused story that Arya tells him,  but Varys would've known instantly that Arya had followed him and Illyrio. 

Varys also knows that Yoren meets Arya that moment. 

From this I can only conclude that Varys let Arya escape from the Red Keep, since he could've known she might escape though the tunnel, and if he wanted her in Cersei's power, he could've made sure she was captured when she got out. 

In ACOK (Tyrion 1 I think) we learn that it was Varys who arranged for Gendry to go with Yoren. Which makes me wonder if Varys wasn't also the one who got Jaqen H'gar in that wagon. It's also likely that he had eyes out,  reporting to him whether Yoren managed to leave the city without losing Gendry, and who else was in this troupe. 

I believe him to be smart enough to figure out that Arya was with them,  despite him telling Ned that his little birds weren't able to locate her. He MUST KNOW how she escaped the castle, and I'm fairly certain he has an idea how she escaped the city. And I have a feeling that he has something tui do with Jaqen H'gar being on that wagon, since we know a lot about his involvement in the black cells. 

Could Varys be in league with the FM?

[Ice Turtle]

I doubt Varys is in league with FM. I don't think he knew Arya spied on him. Varys knows a lot, but not everything, it is possible that he learned that Arya went outside of Red Keep but he likely didn't think much about it. If he learned she was with Yoren, he would have lost her track after Yoren died. The thing about characters like Jon (before becoming LC) and Arya is that big players are not paying them much attention.

[Manderly's Rat Cook]

He wouldn't have been spying on Arya,  but he most certainly was spying on Ned. Arya repeating half of the secret conversation he had with Illyrio, would  definitely ring some bells. There's hardly a way that he would not have known that she followed him,  and thus knew the way out of the castle. 

[CJ McLannister]

It's plausible that he knew Yoren took Arya out of the city.  It's also possible he was keeping tabs on Yoren's party, particularly once troops were sent after them.  It's hard to imagine he had any idea where Arya (or Gendry) went after that.  There's no reason anyone would expect her to end up in Braavos.

[Ice Turtle]

2 minutes ago, Manderly's Rat Cook said:

He wouldn't have been spying on Arya,  but he most certainly was spying on Ned. Arya repeating half of the secret conversation he had with Illyrio, would  definitely ring some bells. There's hardly a way that he would not have known that she followed him,  and thus knew the way out of the castle. 

There is no proof Varys heard that conversation. There seems to be a places in the Red Keep where he can't monitor the conversations. After all Maegor wouldn't wish to be spied upon.  

 

[Manderly's Rat Cook]

52 minutes ago, CJ McLannister said:

It's plausible that he knew Yoren took Arya out of the city.  It's also possible he was keeping tabs on Yoren's party, particularly once troops were sent after them.  It's hard to imagine he had any idea where Arya (or Gendry) went after that.  There's no reason anyone would expect her to end up in Braavos.

I agree, I just suddenly realised how likely it was that he knew Arya followed him that day when I was rereading the Tyrion chapter in ACOK where he already knows about Tyrion's convoy with littlefinger about marrying Myrcella to Robert Arrange (which happened in his solar in the tower of the hand). 

50 minutes ago, Ice Turtle said:

There is no proof Varys heard that conversation. There seems to be a places in the Red Keep where he can't monitor the conversations. After all Maegor wouldn't wish to be spied upon.  

 

He can monitor the conversations in the tower of the hand. Only Mayor's Holdfast is safe from his birds. 

[Manderly's Rat Cook]

57 minutes ago, CJ McLannister said:

It's plausible that he knew Yoren took Arya out of the city.  It's also possible he was keeping tabs on Yoren's party, particularly once troops were sent after them.  It's hard to imagine he had any idea where Arya (or Gendry) went after that.  There's no reason anyone would expect her to end up in Braavos.

I also agree that it's far from certain that Varys has anything to do with the FM, It's the first time I saw any sort of evidence that he knew more about Arya than he was giving away,  and I might have gotten a bit carried away in my enthusiasm thinking why he'd do that. 

I'd love to know Varys's game... 

[Nevets]

Arya's story to her father was so confused that a "little bird" listening in would likely have difficulty realizing its significance.  I do think that Varys was aware of the meeting between Yoren and Arya.  I think it was him who met with Yoren, and he probably told Yoren Arya was loose and to keep an eye out for her at the execution site.  But he probably lost her at that point.  She was well disguised so he departure would have gone unnoticed.  He may be aware that the BwB and the Hound had her, but again, would have lost her track after she left the Hound.

[Manderly's Rat Cook]

1 minute ago, Nevets said:

Arya's story to her father was so confused that a "little bird" listening in would likely have difficulty realizing its significance.  I do think that Varys was aware of the meeting between Yoren and Arya.  I think it was him who met with Yoren, and he probably told Yoren Arya was loose and to keep an eye out for her at the execution site.  But he probably lost her at that point.  She was well disguised so he departure would have gone unnoticed.  He may be aware that the BwB and the Hound had her, but again, would have lost her track after she left the Hound.

The thing is that the little bird wouldn't have to understand,  but Varys would make sense of it. The impression I get is that the little birds report every conversation they see and hear,  no matter if they think it's important or not.  How it's possible that Varys still gonna the time to do things other than listening to their reports is probably the biggest mystery in the books. 

[Nevets]

I honestly don't think Varys is the "Big Bad" who knows everything and has unlimited power. He is a gatherer of intelligence, and sometimes a facilitator.  He probably was aware that Arya knew a secret way out of the castle, but was powerless to stop her from using it.  To stop her, he would probably have to tell others about it, plus there was fighting going on.  Also, they had Sansa and Arya would have been in danger from Joffrey and Cersei, so he probably had no objection to her departure.  In any case, he certainly would have lost track of her once she left the city, especially after Yoren's death.

[Duncan_The_Short]

I think it's possible, but not very plausible, that he could have been keeping track of her right up to the point she left Westeros.  Perhaps he even had an informant on the ship that brought Arya to Bravos.  However, the only way he could have kept track with her after that was if he did have an in with the FM.  Now that I think on it though, if the FM and the Citadel are both working together to prevent magic from coming back, then Vary's would be a natural ally, no?

[BricksAndSparrows]

5 hours ago, Manderly's Rat Cook said:

Then there comes the day that Arya goes missing. Varys must've known that. Later Arya shows up outside the castle gates,  and since we know that Varys has spies in the city gates,  who report to him who enters and leaves the city (which we learn in the Tyrion chapter where Varys pays his first visit to Shae) we can also be certain that he knows who enters and leaves the castle.

You gotta admit, Tyrion's entrance was a bit more conspicuous than Arya's exit...

 

[Manderly's Rat Cook]

1 hour ago, Nevets said:

I honestly don't think Varys is the "Big Bad" who knows everything and has unlimited power. He is a gatherer of intelligence, and sometimes a facilitator.  He probably was aware that Arya knew a secret way out of the castle, but was powerless to stop her from using it.  To stop her, he would probably have to tell others about it, plus there was fighting going on.  Also, they had Sansa and Arya would have been in danger from Joffrey and Cersei, so he probably had no objection to her departure.  In any case, he certainly would have lost track of her once she left the city, especially after Yoren's death.

I don't think he would have betray his secret passage. The only thing he'd have to do was post one /some of his little birds somewhere near the exit (just in case she'd use it) of the passage,  to follow her,  and then report to the Queen where she was hanging out afterwards.

I don't think Varys knows everything,  but I do believe he was aware that she knew the way out and chose not to betray her whereabouts, except (possibly) to Yoren. It's quite curious that Yoren managed to find her in that enormous crowd,  without even knowing she'd escaped the castle,  so it's definitely not unlikely Varys told him she escaped,  when he was making arrangements for Ned and Gendry to go with them.

12 minutes ago, Duncan_The_Short said:

I think it's possible, but not very plausible, that he could have been keeping track of her right up to the point she left Westeros.  Perhaps he even had an informant on the ship that brought Arya to Bravos.  However, the only way he could have kept track with her after that was if he did have an in with the FM.  Now that I think on it though, if the FM and the Citadel are both working together to prevent magic from coming back, then Vary's would be a natural ally, no?

Yeah on one hand I feel it's too far farfetched that Varys is in league with the FM, on the other hand I can't stop wondering why the FM are so interested in Arya, and how Jaqen H'gar knows who she is from the start.  

I know the FM learn to see through a lot of things, and I'm sure any FM would figure out she wasn't a boy,  but it's not that easy to figure out she's Arya Stark, and Jaqen was interested in her from the start... 

[Manderly's Rat Cook]

5 minutes ago, BricksAndSparrows said:

You gotta admit, Tyrion's entrance was a bit more conspicuous than Arya's exit...

 

Agreed, however Ned had his entire household searching for her, Varys would hardly have missed that,  and even if he had,  he had his birds spying on Ned anyway, so he would've gotten a report on Arya returning, her strange account on how she left the castle,  and the meeting with Yoren.

[Nevets]

13 minutes ago, Manderly's Rat Cook said:

I don't think he would have betray his secret passage. The only thing he'd have to do was post one /some of his little birds somewhere near the exit (just in case she'd use it) of the passage,  to follow her,  and then report to the Queen where she was hanging out afterwards.

I don't think Varys knows everything,  but I do believe he was aware that she knew the way out and chose not to betray her whereabouts, except (possibly) to Yoren. It's quite curious that Yoren managed to find her in that enormous crowd,  without even knowing she'd escaped the castle,  so it's definitely not unlikely Varys told him she escaped,  when he was making arrangements for Ned and Gendry to go with them.

He may not have been aware before Arya's earlier escape that it led outside.  If so, he wouldn't know where it came out.  Also, he probably expected Ser Meryn to take her in hand (he almost did), and by the time he found out she escaped, it would have been too late.

As for Yoren, I do believe that Varys told him to be on the lookout for her.  Her father's execution would be a logical place to be, and if I recall correctly, she climbed up on a statue to get a better look.  Yoren could have seen her then, and easily gotten in her way.

[Light a wight tonight]

While I have a feeling, not based on anything textual, that Arya was destined to be trained by the Faceless Men, it don't think Varys was part of the mechanism. Being captured by Gregor's men, escaping from Harrenhall, being captured by Sandor and him getting nearly killed in the inn, etc, etc, none of this could have been effected or even monitored by Varys.

[Yollo/Hugor Hill/Tyrion]

1 hour ago, Duncan_The_Short said:

I think it's possible, but not very plausible, that he could have been keeping track of her right up to the point she left Westeros.  Perhaps he even had an informant on the ship that brought Arya to Bravos.  However, the only way he could have kept track with her after that was if he did have an in with the FM.  Now that I think on it though, if the FM and the Citadel are both working together to prevent magic from coming back, then Vary's would be a natural ally, no?

I frankly don't think that Varys has informants literally everywhere you can think the man is not a god he only has little birds where he chooses to put them and they don't always get back to him in good time. For instance when Stannis and Balon Greyjoy both stopped any ships or ravens from leaving their respective strongholds Varys was unable to report on what they were up to and thus had no idea what they were going to do. he definitely has a massive number of informants they just are'nt literally

 

6 hours ago, Manderly's Rat Cook said:

From this I can only conclude that Varys let Arya escape from the Red Keep, since he could've known she might escape though the tunnel, and if he wanted her in Cersei's power, he could've made sure she was captured when she got out. 

Varys was a little preoccupied that day seeing as they queen had guards sacking her own keep and killing northmen left and right. he was right there in the throne room when it happened i doubt he was allowed to leave and frankly Arya was a child it wasn't that hard for him to loose track of her in all that chaos and after that what's one child among thousands in Flea Bottom? If it wasn't Arya she probably would've died there and once the war started it becomes nearly impossible to track any one person's movements. Varys' little birds work best when things are quiet, not during a massacre and definitely not when the king is starting a war for no reason.

[Lost Melnibonean]

I like your reasoning, but Varys's resources are not limitless. I wonder if he kept tabs on Arya. He might not have been paying that close attention to the little girl. 

[The Wull]

Agree with the others - there was just too much going on at that time for him to keep tabs on every person in KL 24/7.  He probably knows a lot of what goes on in the areas like the Tower of the Hand where important people tend to gather, but we know Arya loves to explore the back passages.  It's a lot more unlikely that he'd have informants stationed in the sewers that nobody knows about except for him.  

I think his knowledge stretches belief as is.  We know he bribes people, is good with disguises, has children spy for him, and utilizes secret tunnels to listen in on conversations.  Even so, the idea that one man could take in all that information, or have enough time in the day to listen to it all, seems extremely unlikely.  

[Dorian Martell]

14 hours ago, Manderly's Rat Cook said:

I believe Varys knows a lot more about Arya's whereabouts than we're led to believe. 

Could Varys be in league with the FM?

Not a chance.
As a child of winterfell, Arya would be beyond valuable to the crown. If Varys was aware of her he would have tried to capture her.