M'Vila has been linked with a transfer to Liverpool on a number of occasions, but Bilyaletdinov claims that the midfielder's attitude prevents him from taking his game to the next level.
"In January M'Vila behaved badly - one day he trained, one day he didn't," the Rubin boss told France Football.
"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."
M'Vila moved to Rubin from Rennes in January 2013.