A host of clubs including Queens Park Rangers, Fulham, Reading and Tottenham are understood to be keen on luring the France international to the Premier League.
However, Russian pair Zenit St Petersburg and Rubin Kazan are also keen with the latter believed to be favourites for his signature.
After M'Vila played in the win over Bastia, the club's general manager Pierre Dreossi was asked about the midfielder's future.
Dreossi would not reveal M'Vila's likely destination was, but admitted he was unlikely to play for Rennes again.
"There is a good chance that this is the last game Yann M'Vila will have played for Rennes," he said.