The Ligue 1 outfit were first linked with the French striker in July last year, and rekindled their interest again in March.
But a report in L’Equipe suggests the Stade Velodrome side have ended their interest in the France Under-21 international.
The article centres on Marseille’s pursuit of Nice striker Mario Balotelli.
OM are understood to be keen on landing the Italian forward before the end of June, but are thought to have approached two other players in case a deal for the former Liverpool and AC Milan striker falls through.
However, Dembele is not thought to be one of them, with Sevilla’s Wissem Ben Yedder and Porto striker Vincent Aboubakar mooted as possibilities.
The article suggests that the pair are admired by the Marseille hierarchy but the club has not taken the interest further at the time of writing.
Dembele, who began his career with Paris Saint-Germain before a spell with Fulham, has been linked with a string of top clubs including Villarreal, Roma, Chelsea, Arsenal, Manchester City and Brighton.