Payet was reported to have been the subject of an €8 million bid from Premier League outfit, which it was claimed Marseille had accepted.
However, the former Lille man has ruled out joining the Welsh club and is determined to showcase his talents at the Stade Velodrome.
He told L'Equipe: "With all respect due to Swansea, I want to stay at OM.
"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 believes Marseille are keen to offload him for financial reasons and due to what he deemed to be a disappointing 2013-14 campaign.
"I'm being pushed out of the club, but I can understand that. There is an economical reality behind that," he added.
"My first season was average. I've expected better from myself and I guess it's also their case."
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