The former Arsenal man is a free agent at the end of the season and is thought to be considering his options having rarely featured for the Serie A outfit this year.
The Frenchman's tenure at the San Siro has been plagued by injuries, and he is now considering a return to the Premier League, according to ClubCall.
Saints boss Mauricio Pochettino is supposedly keen on bringing in the 29-year-old, in order to add some experience to his largely young midfield.
Villa boss Paul Lambert is also monitoring Flamini's situation, but it is expected that the player would reject a move to Villa Park should they get relegated this campaign.
Flamini made over 150 appearances for the Gunners during a four-year spell before heading out to Italy.