The 23-year-old has again been linked to the Premier League, but Ribat Bilyaletdinov insists the player's homesickness affects his performances.
The midfielder joined the Russian outfit for a fee of around 12 million euro in January 2013, but Bilyaletdinov admits the 23-year-old has struggled to settle at the club and is not fitting into the side.
Liverpool has been linked with M'Vila in the past, and speculation that he could move to Anfield has been reignited recently, but the Rubin boss feels the intensity of football in England would not suit the France international.
"He has to prove his value and work like everyone else. I don't mean that he doesn't work, but we can see that he misses France," Bilyaletdinov told France Football. "In January M'Vila behaved badly - one day he trained, one day he didn't.
"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, now I haven't seen him for a while. I have been told he is in France to heal an injury. Even if he is back to full fitness, I don't know where to play him."