The France international has continually been linked with a move away from Rennes, with clubs such as the Gunners and Inter believed to be interested in signing the holding midfielder.
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The 22-year-old was one of the most sought-after players in Europe before Euro 2012, and his club supremo has insisted he is not attempting to deny the player a transfer to a bigger club.
"We have an agreement with him that allows him to leave this summer, but we have not yet received any concrete offers for him," Saint-Sernin was quoted as saying by RMC.
"Several clubs have enquired about him, but there are no formal offers. He is still a Rennes player. Several big foreign clubs are interested, but we are not blocking anything as there are no offers yet."
M'Vila has a contract with Rennes until the summer of 2015, and an offer in the region of £15.75 million could be required to lure him away from his current club.