The 22-year-old impressed on loan at Sunderland during the 2015-16 campaign, with the 22-time France international appearing in 37 of the club's 38 Premier League matches in that season.
M'Vila's contract with Saint-Etienne will expire at the end of next term, and the midfielder has not ruled out the possibility of playing in the Premier League once again.
"I'm only 27 years old," he told SFR Sport. "I signed with Saint-Etienne until June 2019. I am very happy there and I think only about football, about being on the pitch. My agent takes care of the rest.
"I spent an amazing year in Sunderland. [The Premier League] is the best championship in the world. Why not [return to England]? Only God knows if I'll be at Saint-Etienne next season. For the moment, I do not know.
"With the board and the coach, we are dreaming of qualifying for Europe. On May 19 [after the season has finished], we can sit around a table and discuss."
M'Vila joined Saint-Etienne from Rubin Kazan during the January transfer window.