Flamini's contract runs out at the San Siro at the end of the season and despite featuring regularly this season, the Frenchman is expected to leave Milan.
A host of clubs including Southampton and Aston Villa have been linked with a move for the 29-year-old, who has admitted that he is open to a reunion with Elie Baup's side.
He told L'Equipe: "OM is a club that is in my heart.
"Now it has the opportunity to become a big club. It enjoys a high standard of facilities and the new stadium looks magnificent, and it can count on exceptional supporters.
"So a return to Marseille in the short-term, I don't know, but you can never say never."
The former Arsenal midfielder has made 16 appearances for Milan this season in all competitions.