Izvestia says Everton want the 23-year-old M'Vila to replace Gareth Barry in the Toffee's midfield when his loan expires at the end of the season, and play alongside James McCarthy as one of two holding players.
Agent Werner Baader said: "Indeed, many European clubs are interested in Yann, including English clubs.
"This is normal for a player of such a high level.
"At the moment M'Vila is under contract with Rubin, and the club are satisfied.
"Let's see what happens in the winter [transfer window]."
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