Arsene Wenger wants to sign the 21-year-old French international as an ideal partner in the centre of midfield for Alex Song.
Wenger has been pushed to begin negotiations after Bayern Munich and Inter Milan showed a keen interest in M'Vila.
The midfielder has been capped 18 times by France and could cost £22 million, with three years remaining on his current contract.
Arsenal became favourites for his signature after the player admitted it would be difficult to turn down a move to the Emirates and his manager Frederic Antonetti believes he is likely to move in the summer.
Source: DSG