General manager Pierre Dreossi admits the club want his situation resolved this weekend, and that an agreement with the Russian club was most likely.
Queens Park Rangers have been in talks, but now Dreossi says a new bid from England has come, and he would only confirm that it was not from Newcastle.
Arsenal, Tottenham, Fulham and Reading have also been linked with moves for the 22-year-old midfielder in recent weeks.
"It is complicated, but we are still in negotiations," said Dreossi.
"It is not agreed yet, there are delays in payment, everything. I hope we will find a solution.
"Also a new offer came in England and that could be interesting but Rubin Kazan is the priority, and we are negotiating.
"I expect the player to tell me he has reached an agreement with the club so we can finish the negotiations."
Dreossi feels QPR are now out of the running, adding: "QPR? I met with them for a long time [on Monday] but I think they will withdraw and I have not heard from them since.
He would not reveal the new bidder from England, saying "The new English club? This is not Newcastle - but no matter, M'Vila will leave and it will be finished before Saturday's game."