Inter sporting director Piero Ausilio stated last month that the club were in talks with Rubin over a move for the France international.
And those discussions appear to have progressed well, with Icardi confirming he had seen M'Vila on Tuesday and suggesting that the 24-year-old was due to undergo a medical.
"I saw M'Vila today, he's having a check-up," the forward told Sky Sport Italia.
Gary Medel could also be on the way to San Siro, according to his Chile team-mate Mauricio Pinilla.
Medel has been linked with a move away from Cardiff City following the Welsh club's relegation from the Premier League last season.
Pinilla is quoted as telling Corriere dello Sport: "Medel told me that he could go to Inter and he asked me for information about Italy."