23-year-old M'Vila - a senior French international with 22 caps - has been linked with both Arsenal and Liverpool in recent months, but Rubin coach Rinat Bilyaletdinov has admitted that he told the player that a move to the Reds wasn't exactly a good fit.
"In January M'Vila behaved badly - one day he trained, one day he didn't," he told France Football in an interview that was quoted by The Daily Express.
"Maybe his agents had promised him something. He thought he was already in Liverpool. I told him: 'It is not your level. If you go, you will be on the bench'. He was very disappointed."
Such a jibe over M'Vila's ability would surely have been particularly painful coming from anyone, never mind his own manager.
The former Rennes star - who signed for Rubin in January 2013 - does not appear to have much of a sustainable future at Kazan Arena.
"Now I haven't seen him for a while. I have been told he is in France to cure an injury. Even if he is back to full fitness, I don't know where to play him," Bilyaletdinov continued.
Whether or not Liverpool plan to make a move for M'Vila - particularly given his lack of regular football in recent months - during the next transfer window remains to be seen.
With Brendan Rodgers' side sitting pretty at the top of the Premier League with just five games of the season remaining, it is surely likely that he will be looking to entice several new recruits to Anfield this summer.
However, with Bilyaletdinov appearing to raise questions over his attitude and application, it could be that Liverpool are better of focusing on other potential targets in preparation for a return to the Champions League.