The 24-year-old enjoyed an eye-catching 2012/13 campaign, with his first taste of the French top flight seeing him end the season with 10 goals and five assists.
Marseille are now reported to have lodged a €7million (£5.9m) bid for a player who was schooled in their academy ranks up until the age of 15.
Alessandrini admits he would find it impossible to pass up the opportunity to return to Stade Velodrome, but he is contracted to Rennes until 2016 and will not be rocking the boat.
He told L'Equipe: "The fact that l'OM are interested in me is amazing because it is the club in my heart.
"I grew up at Marseille. Coming back would be a great opportunity for me. I really want to come back.
"I know what I owe Rennes, they offered me a start in Ligue 1. I have a lot of respect for the officials, the fans and my team-mates, but when a club like l'OM wants you, you join another world. You can play in the Champions League.
"I don't want to start a war, though, as I have not been brought up that way. I feel really fine at Rennes."