The France international proved a thrilling addition for the Hammers since his arrival in the summer of 2015, scoring 15 goals in his first season in England.
However, West Ham have made a terrible start to the new campaign, winning just three of their first 11 games and currently sit four points above the drop zone.
That has sparked fears that Payet could opt to leave when the transfer window opens.
Payet signed a five-and-a-half-year contract in February, but in an interview with French television show Telefoot he said: “We’ve had a very poor start. Leave in January? I’m asking other questions right now but I’ve closed the door to nothing.”
He continued: “Until now, I always chose my clubs depending on the sports project. I work like that. Until I can play at a level like this, it will be the case.
“Go to PSG or Marseille? For now, they have not come to me, so I do not ask myself.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies