The Ghana international, 22, had been linked with a transfer after changing agents.
And he reacted angrily to the suggestion that he was angling for a move away from OM by telling the club website: "It’s absolute rubbish".
"Changing agent is one thing, changing club is completely different," he added.
"To say changing agent means obligatorily changing club is just a lazy association and doesn't reflect the reality of the situation."
"I never said I wanted to quit Marseille."
Ayew scored 16 goals in all competitions for Marseille this season, having hit 13 in the prior campaign.
His current deal expires in three years and has a buyout clause of 18 million euros.
Marseille won the Coupe de la Ligue last season but otherwise had a poor campaign, finishing 10th in Ligue 1.