Reports emerged earlier this week suggesting that Payet's representative had demanded a significant pay rise for his client, who has shined in the Premier League following his summer move from Marseille.
Payet signed a five-and-a-half-year deal in June and coach Slaven Bilic urged the club's hierarchy to reach an agreement with the playmaker as they attempt to keep their key players happy ahead of their move to the Olympic Stadium next season.
And the club clarified in a statement on Tuesday that initial talks over a new contract have been "amicable and productive".
READ MORE | Bilic wants new contract for Payet
"Following reports in today's media, West Ham United would like to clarify that at no time have Dimitri Payet or his agent made any demands to the club over a new contract," the club said.
"However, the club can confirm that due to Dimitri's outstanding impact since his arrival at the Boleyn Ground, they have initiated amicable and productive talks about an improvement and extension to his contract.
"Those talks are progressing well and it is hoped they can be concluded shortly.
"Dimitri would like to make clear that he is very proud to play for West Ham United and he appreciates the support he has received from the Board, manager and fans since he joined the club in the summer."
Payet has six goals and five assists from 22 appearances this term, having been sidelined for almost two months by an ankle injury sustained in November.