It's no secret Littlefinger has been playing his games right from the start, and his favorite target is the Stark family. In an interview with Entertainment Weekly, Game of Thrones star Aidan Gillen confirmed the fan theory that Littlefinger recognized Arya in Season 2 during his meeting with Tywin Lannister. Remember, at the time, the youngest Stark daughter was posing as a peasant girl and serving as the Lannister patriarch's cup-bearer at Harrenhal. Littlefinger had the opportunity to expose her identity, but he kept mum.
At least that's what Gillen believes. The Game of Thrones star told EW,
The actor didn't elaborate on why his duplicitous character chose not to blow Arya's cover. However, it's safe to assume he didn't feel there was anything to gain by exposing her. Even back in Season 2, Littlefinger was eager to gain Sansa's favor. If he had revealed her sister to Tywin, and Arya had been reunited with Sansa, the eldest Stark daughter would no longer have been isolated. Without the isolation, she would have been less malleable too. Another possibility is that revealing Arya's identity simply didn't match up with his goals at the time. Every move Littlefinger makes is calculated, and Arya wasn't part of his plan.
With Littlefinger at Winterfell, and Arya back in Westeros, it's entirely possible these two characters' paths will cross again. At the moment, the sneaky Petyr Baelish is spending every waking moment trying to turn Sansa against Jon. Gillen revealed Littlefinger's machinations will only become more persistent in Season 7:
Jon is already suspicious of Littlefinger's interest in his sister. If Arya returns to Winterfell as well, it will be interesting to see how she feels about Petyr now. Every move Littlerfinger has made so far has been in service of bringing him closer to Sansa and a true position of power. However, if Arya does reunite with her family, Littlefinger should watch his back. Just because he didn't reveal her identity to Tywin all those years ago doesn't mean she's forgotten everything he's done to her family.