According to the Metro, there are concerns about M'Vila's recent behavior.
Wenger is said to be unhappy with the 21-year-old's involvement in a spat with France coach Laurent Blanc during Euro 2012, which also involved Hatem Ben Arfa, Jeremy Menez and former Gunner Samir Nasri.
It's just the latest in a long line of incidents which have clouded M'Vila's character, with plenty unimpressed that he's been arrested three times in the past two years for various offences including attacking a restaurant owner after a bout of road rage, using prostitutes and punching a teenage boy who had shown an interest in his sister.
Should Arsenal sign M'Vila?
Young players are going to make mistakes, and manager Arsene Wenger is someone who can mentor M'Vila.
Expectations of having to perform at a high level in the Premier League would help make M'Vila focus and realize that he must act like a professional wherever he is.
Arsenal have already made some impressive transactions in the transfer window to improve the squad for next season.
French striker Olivier Giroud, who was M'Vila's teammate with France at Euro 2012, was the latest signing for the London club. The Gunners also signed German forward Lukas Podolski earlier this year.
Bringing M'Vila to the Emirates would be another fantastic signing for Arsenal after last summer's transfer window was a disaster from start to finish.