It is being reported in French newspaper L’Equipe that OM will offer Celtic £13.5 million for the forward.
Marseille hope that the offer will be enough to secure the player’s transfer with the deal getting done in France.
The Ligue 1 side saw a move for former Manchester City striker Mario Balotelli fall through earlier in the summer, while they have been linked with Valencia and Italy forward Simone Zaza.
Dembele was linked with a move to Marseille last year and earlier this summer but interest cooled when attention switched to Balotelli from Nice.
The French Under-21 international came off the bench on Tuesday in Celtic’s 2-1 defeat to Greek champions AEK Athens as the side dropped out of the Champions League and into the Europa League play-off round.
The 22-year-old, signed from Fulham in 2016, has scored 50 goals in 91 appearances for Celtic and has been linked to moves to numerous clubs.