It is understood Spurs have proposed a fee of £12.7m with add-ons, though Rennes want an unconditional £15m.
The French club replied to Tottenham's written offer by suggesting face-to-face talks but are yet to hear back.
Another unnamed Premier League club have registered interest in signing M'Vila, although it is not Arsenal.
After M'Vila rejected moves to Zenit St Petersburg and Shakhtar Donetsk, Tottenham's bid is the only one on the table at present.
M'Vila, who featured in his side's 3-2 victory over Bastia on Saturday, hoped to travel to London early this week to discuss personal terms and undergo a medical - but the transfer has not developed as swiftly as expected.
If he does join Tottenham it could see Rafael van der Vaart leave White Hart Lane, despite the Dutchman occupying a more advanced position on the pitch.
Van der Vaart has been linked with a return to Hamburg while fellow midfielder Luka Modric is expected to sign for Real Madrid.
Spurs are further depleted in that area by Scott Parker's Achilles injury, while Tom Huddlestone could join Stoke on loan.
M'Vila had been linked with Arsenal but there has so far been no concrete interest from the Gunners this summer.
Reports in France suggest there has also been recent interest from Everton and Newcastle.
M'Vila made 61 appearances for Rennes and France last season, featuring in three of his country's four Euro 2012 matches.
Yann M'Vila
Born: 29 June 1990 Amiens, France
Position: Midfielder
Rennes: 2009-2012 (110 appearances, two goals)
France caps: 22 (one goal)
Not exactly a prolific goal scorer ! ! !
Thu Jan 21 2021, 20:01 by BazSpur
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