Payet’s reputation has continued to grow due to his performance at Euro 2016 for France.
Payet has been his nation’s best player throughout the international tournament to date, and his performances have caught the eye of some high profile teams.
Real Madrid have been strongly linked with the 29-year-old, but Parlour believes that Payet may be suitably excited by West Ham’s future plans to remain at the Olympic Stadium.
“West Ham will be delighted that he signed a new contract, but contracts don’t matter these days,” Parlour said.
“He’s lit up the Euro’s so far, but he might be looking forward to the new stadium with Slaven Bilic. He might want to stay at West Ham.”
Payet signed a contract at West Ham last season, which is due to keep him at the London club until 2021.
West Ham are, therefore, under no pressure to sell the attacking midfielder, but they realise that holding on to him could be difficult if Madrid do submit an offer.
West Ham have reportedly slapped a £60 million price tag on Payet to try and fend off any interest.
Payet scored nine goals and claimed 12 assists for West Ham in the Premier League last season.