The 22-year-old has been touted for a move away from the club for some time, with QPR boss Harry Redknapp previously confident of luring M’Vila to the club.
Goal.com also exclusively revealed on January 18 that the Hoops’ Premier League rivals Tottenham were considering a late swoop to bring him to White Hart Lane.
However, both clubs now look set to be miss out after the Ligue 1 club made an announcement on their official website
|WEDNESDAY TRANSFER ROUND-UP
|4/1||MK Dons are 4/1 with William Hill to beat QPR in the FA Cup
Earlier, Rubin's vice-president Kamil Ishakov admitted the player was close to sealing a switch, but for the ironing out of the final details of the deal.
He told Sport-Express: "M'Vila attracts many European clubs. In England, clubs such as QPR, Fulham and Arsenal have, like Rubin, made concrete proposals.
"[But] Negotiations are currently in our favour. There are still some details, including the final results of the medical visit which takes place in Rome. Once the results are published, all will be decided. It is possible that he could sign the contract tonight."