The 22-year-old has been heavily linked with a move to North London, with both Arsenal and Tottenham making offers for the player.
The Gunners were looking at M'Vila as a replacement for Alex Song, who joined Barcelona earlier this month, but have recently given up on the player.
Spurs came in for him more recently and, according to Rennes chairman Frederic de Saint Sernin, ended their interest last night.
De Saint Sernin said: "He's not going to England.
"Tottenham gave up on the player at 7.30pm last night. It's 95% sure he will stay at Rennes."
M'Vila has 22 caps for the France national side.