Rumor has it that Ozil would like a 300k per week deal to stay at The Emirates stadium. It is said that Arsenal are now "very, very, close" to a breakthrough.
While manager Arsene Wenger has suggested neither will leave, his former player Petit believes both men could be angling for an exit in the winter window. Ozil had joined Arsenal from Real Madrid in summer 2013, for a then-club record £42m.
United want to convince the Gunners to sell in January to avoid watching him go for free next summer.
Arsenal have been on a decent run of late, despite Saturday's disappointing home defeat to Manchester United, and they sit in fifth position in the Premier League table, having already qualified for the last 32 of the Europa League as group winners, with one game to spare.
Giroud admits Arsenal must do everything they can to keep Ozil
Ernesto Valverde's men are considering a €20m swoop for the World Cup victor in the January transfer window, though Arsenal boss Wenger recently insisted that the German will stay in north London until the end of the season, alongside fellow wantaway Alexis Sanchez.
But Arsene Wenger's unwillingness to lose him for nothing could well forge a deal for Jose Mourinho's side, should no one else move for him.
Ozil is likely to feature against Southampton in the Premier League on Sunday.
Although holding on to Ozil may be a big coup for Arsenal, it might not be the best signing for Man Utd.
With both Henrikh Mkhitaryan and Juan Mata struggling at Old Trafford, Ozil could be the flawless fit for the No 10 position with United chasing City at the top.