After progressing through Marseille's youth set-up, Andre played for the senior side between 2007 and 2015 before joining English outfit Swansea City.
The 27-year-old currently plays for West Ham United following a summer move last year.
''If the owner and the fans, who are very important for the club, have the same vision, Marseille will once again become a big club," Abedi told Le Parisien.
"We’ll see how the recruiting goes this summer, and where the club wants to go.
''It’s possible that Andre returns to Marseille one day. He’s one of the club’s children. He developed at Marseille.
"He loves the shirt, and the fans know he’s ready to do anything for his club.''
Andre twice won the League Cup during his days at Marseille, in addition to two Super Cup titles.
Abedi, on the other hand, is highly remembered for helping Les Olympiens win the Uefa Champions League in 1993.