It has been reported by the British tabloid that the Marseille winger has been offered a five-year deal worth almost £60,000 per week.
However, the 28-year-old allegedly wants £80,000 a week to put pen to paper on a contract with Premier League outfit West Ham.
It will be interesting to see if West Ham increase their offer and sign Payet, or they look for alternatives who would be happy with a salary of £60,000 a week.
Payet has been on the books of Marseille since 2013 and is a France international.
The former Lille 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.