The 35-year-old spent the 2012-13 season on loan at the French club after falling out of favour at then-Premier League club Queens Park Rangers.
"The supporters immediately accepted me when I arrived," said Barton, speaking in a video posted on the club's official website as part of the documentary Marseille: A Football City.
"They must have perceived something in my character and personality that they liked.
"I'd love one day to pull the jersey on again and if I can't do it as a player then I would love to do it as a coach or manager."
Barton is not able to return to the game until his ban for breaching betting rules ends in June 2018.