The Italy international expects his team-mate to snub a return to Serie A and remain with les Parisiens for the foreseeable future
Nerazzurri boss Walter Mazzarri admitted he would be interested in signing the former Napoli forward if he became available but Veratti is convinced Paris is where his team-mate will remain.
"I have no doubts that Lavezzi will stay here," the Italy midfielder told Sky Sport Italia.
"He had a bit of a difficult period at the start of the season, but he's all smiles again in training now. He is one of those players who really enjoys the game.
"I think that he will stay at PSG for many more years."
Lavezzi, 28, joined PSG from Napoli in the summer of 2012 but has not yet replicated his form in Naples having scored just five times in 40 appearances for the club.
The attacker's current deal runs until June 2016.