Dimitri Payet says he is "not closing the door to anything" when questioned on a possible January exit from West Ham.
The playmaker was an outstanding performer during his first season in England, helping the Hammers to finish seventh and earning a prominent role in France's run to the final of Euro 2016 on home soil.
West Ham have struggled to recapture their best form since moving to London Stadium, failing to qualify for the group stage of the Europa League and winning just three of 11 Premier League matches so far this season.
That has led some observers to suggest Payet could target a switch to a club competing for major honours.
And during an appearance on French television programme Telefoot, the 29-year-old was asked directly if he might leave West Ham during the mid-season transfer window.
"I'm asking myself other questions, I have ambition, but I'm not closing the door to anything," he said.
"It's always the sports project that interests me. For now, PSG [Paris Saint-Germain] and OM [Marseille] did not come to me [with an offer]."
Of the Hammers' poor opening to 2016-17, he added: "It was a very bad start with West Ham, we're trying to get into the top half of the table."
Former Bayern Munich and France defender Bixente Lizarazu was appearing alongside Payet on the programme and suggested the attacking midfielder, who left Marseille to join West Ham in June 2015, was ideally suited to the Premier League.
"I think the future of Dimitri will always [be in] England. He's made to play there."
Payet also backed his international team-mate Antoine Griezmann of Atletico Madrid to feature in the top three of France Football's prestigious player of the year award, the Ballon d'Or.
"I would like Griezmann to be on the podium for the Golden Ball," he said.