The Frenchman explained that the returns of Abou Diaby and Jack Wilshere mean he will not bid for the 22-year-old and claimed that he is unaware of reported target Santi Cazorla
The Gunners have long been linked with a bid for the 22-year-old, although his club recently revealed that they have yet to receive any formal offers for the player.
Wenger has now moved to quash suggestions he will try to bring the France international to London, provided that Abou Diaby and Jack Wilshere do not suffer any setbacks in their respetcive returns from injury.
Asked whether he was still interested in M'Vila, the 62-year-old told reporters: "No. We wait for Diaby and Wilshere. When he is fit, Diaby is the first name on the French team sheet.
“When you look we have Alex Song, Aaron Ramsey, Francis Coquelin, Diaby, Wilshere and Mikel Arteta.
"We are not short if Diaby and Wilshere are coming back. If we have setbacks in pre-season, it could be different."
Wenger was also coy on suggestions he could make a move for Malaga winger Santi Cazorla, who has been linked Tottenham.
When quizzed on his possible interest in the Spain international, he quipped: "I don't know this guy!"
Arsenal are currently in Kuala Lumpur as they begin their pre-season preparations with a tour of the Far East.