The two sides agreed a £6.7m fee for the playmaker earlier this week as manager Garry Monk seeks to reinforce his Swans squad ahead of the 2014-15 season.
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“Am I attracted by Swansea proposition? With all respect I have for Swansea I am absolutely not attracted,” he told L'Equipe. “Since first contact between the club and my agent, I declined the offer. I want to go on at l’OM.
“Since the start, I was sure [I wanted] to stay. I immediately talked to the chairman. Even if the press stated I didn’t make my choice so far. Those rumours must be stopped.
“Indeed on a financial level the offer is very attractive. But being 27, I still have sporting objectives and I decided to stay. If a very big club wanted to contact me it would have done so already. I was average last season, I should have done much more to be a serious target. You never know in football but today I can say I will stay at l’OM 100 per cent."
Payet also believes he can be a key asset to new boss Marcelo Bielsa, who was appointed in May, as the club seek to improve on last season's sixth-placed finish.
“Bielsa told me very few things, except he wants to make me improve,” Payet added. “He wants me to be steadier and not only to be good for half a season.
“He has played me as a playmaker so far, a position that I like. I believe he believes in me and that is also why I want to stay at Marseille.”