The France international has risen to prominence after a fine debut season for the Hammers, scoring nine goals and providing 12 assists in 30 Premier League appearances following his switch from Marseille in July 2015.
Payet has been linked with league rivals Chelsea and Manchester City, who will both be under new management next term, while Paris Saint-Germain are also rumoured to be interested in acquiring his services.
The 29-year-old produced another moment of magic on Friday when he scored a late winner for Les Bleus in their Euro 2016 opener against Romania to secure a 2-1 victory, and his representative, Mark McKay, insists Payet's stock has risen even higher now.
"As far as I am concerned, he's been happy at West Ham and it's down to West Ham that he's in the position that he is in," McKay told Sky Sports.
"When he first came last year we hoped for the best with him. We knew that he was a really good player, but I don't think anyone could really expect what he has gone on to do in the Premier League so far.
"He's doing great now for France and to get him now, you've got to be talking ridiculous money. But football is football, so you never know."