Hammers manager Slaven Bilic said earlier this month that Payet did not want to play for the club, but added the 29-year-old would not be sold.
But, after rejecting two bids from Marseille and signing Robert Snodgrass, West Ham have decided to sell the France international.
Payet joined West Ham from Marseille for £10.7m in June 2015.
He excelled in his first season with the London club, scoring 12 goals and earning a nomination for the PFA Players' Player of the Year award.
In February 2016 he signed a new contract to tie him to the Hammers to the summer of 2021.
He then helped France reach the final of Euro 2016, where the hosts were beaten by Portugal.
However, Payet has scored just three goals for the Hammers this season.
West Ham forward Dimitri Payet is set to rejoin former club Marseille after the clubs agreed a £25m fee.