Payet has enjoyed a wonderful first season at Upton Park and established himself as one of the finest players in the Premier League.
The Hammers believe that Payet’s reputation will only increase at Euro 2016, as he is likely to play a key role for France.
Payet has seemingly forced his way into Didier Deschamp’s starting line-up, and he seems likely to play regularly for the hosts at the international tournament.
West Ham realise that if Payet has an eye-catching European Championships it could be tough to keep hold of him, but they are determined not to lose their talisman on the cheap.
Payet signed a new contract at West Ham mid way through last season, and the London club are under no pressure to sell.
Slaven Bilic’s side are said to value Payet at £60 million, which means that he is out of the price bracket for most clubs.
West Ham reportedly believe that the only clubs who would have a chance of signing the 29-year-old would be the likes of Real Madrid or Barcelona.
Payet scored nine goals and claimed 12 assists in 30 Premier League appearances last term.