“The 28-year-old France international playmaker is available for around £6m and has been considered by Everton but is more keen on a move to London,” states a report in The Daily Mail.
This follows a recent report which claimed that West Ham and Payet cannot agree on wages, which is why there is a delay in completing the transfer.
According to The Sun, the Marseille winger has been offered a five-year deal worth almost £60,000 per week.
However, Payert allegedly wants £80,000 a week to put pen to paper on a contract with the London outfit.
Payet has been on the books of Marseille since 2013 and is one of the better players in Ligue 1.
The former Nantes star scored seven goals and created 134 chances in 36 Ligue 1 appearances in the recently concluded 2014-15 season.
The 28-year-old had a pass accuracy of 80% and a shot accuracy of 47%, and won three headers, 66 dribbles and 17 tackles.