Swansea City were believed to have held talks with the French giants and agreed a €8m fee for the 27-year-old - who was said to be unsure about moving to England - earlier this month.
However, Payet has now revealed that he has no intention of leaving the Velodrome, but admitted that he would have jumped ship if a bigger club than the Welsh team had come calling.
"With all respect due to Swansea, I want to stay at OM," Payet told L’Equipe.
"I said no to my agent right after the first contact. I told the president from the start that I want to stay. Despite that, the press still says that I'm hesitating.
"If a bigger club had shown interest in me, I would be gone by now. But I had an average season and you should do more to be coveted.
"In football, you can never say never, but I feel like I'll stay at Marseille, 100 per cent."
Payet joined from Lille in 2013 and scored eight league goals for Marseille last term, but Payet believes that his mediocre performances since joining the nine-time French champions explains why the club are willing to sell him.
"I'm being pushed out of the club, but I can understand that. There is an economical reality behind that," the Frenchman continued.
"My first season was average. I've expected better from myself and I guess it's also their case [too]."