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 it has 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 respective returns from injury.
"No. We wait for Diaby and Wilshere. When he is fit, Diaby is the first name on the French team sheet," the 62-year-old told reporters when asked whether he was still interested in M'Vila. “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 preseason, 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.
"I don't know this guy," he quipped.
Arsenal is currently in Kuala Lumpur as the club begins it preseason preparations with a tour of the Far East.
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