Ramsey is in the market for a new club after learning he is surplus to requirements at Juventus.
Petit told the Mirror: "Ramsey wanted to leave, what is the point in coming back?
"He is on big wages at Italy and I'm pretty sure Arsenal won't be able to give him that. That is why he left for Italy."
Ramsey spent 11 years in north London, winning three FA Cups in this time.