Both North London clubs have been strongly linked with the Frenchman after the player made it clear that he wanted to leave the Ligue 1 outfit.
The Gunners were reportedly close to a deal for M'Vila prior to Euro 2012, with Spurs having had a bid of nearly £13m rejected by Rennes earlier this week, and current manager Frederic Antonetti believes that his side could now keep the defensive midfielder.
"We have had some contact but nothing more than that. The more time goes on the more we can think he will stay," said Antonetti.
"Now, as I have been saying for some time, we know Yann could still go in the final week of the transfer window."
The 22-year-old has 22 caps for the France national side.