Payet, who has played 15 times for France, has scored six league goals and provided five assists in 18 games for the Hammers this season as the club has mounted an increasingly credible challenge for a top-six finish.
West Ham manager Slaven Bilic said earlier on Thursday that Payet was very close to signing a new deal when he previewed Saturday's league clash at struggling Norwich City.
The manager also spoke out in support of cheaper tickets for fans after a mass walkout at Anfield last weekend resulted in Liverpool's owners backing down on plans to implement a significant increase in prices next season.
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"Football is not polo or golf. It is not a sport for the upper class," Bilic said. "It's about a balance. In the Premier League you get a lot of money from TV and sponsorship, so tickets should be a good price for fans."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by David Goodman and Ken Ferris)
