"Dimitri has had an outstanding year and has become a vital player for France and I am so proud that he is a West Ham player," Sullivan told the club's official website.
"He has played 16 times for his country in 2016, scoring seven goals and assisting five more, and inspiring them to the final of the European Championship."
Payet, however, has struggled to rediscover his best league form this season, having scored just once in the opening 11 league games as West Ham sit 17th in the table, a point above the relegation zone.
"Dimitri signed a new long-term contract in February, pledging his future to this club, and it is very much our intention that he remains with us for years to come," Sullivan added.
West Ham travel to face London rivals Tottenham Hotspur, who are fifth in the table, on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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