Dimitri Payet could be the subject of the third offer from Marseille as the French club aim to buy back the wantaway midfielder according to Sky Sports.
Talks on Monday, after a second offer from the French side of around 320m but both clubs failed to agree on the transfer for the 29-year-old.
Payet was also forced to train with Under-23s on Wednesday.
The playmaker revealed he wants to move back to France, in particular, Marseille, due to family reasons and it is not fueled by money.
But the Hammers want an estimated £30m for the key player with Marseille's previous offers failing to meet that quota.
Slaven Bilic said last week Payet told him of his desire to leave the club and was left out of their 3-0 victory over Crystal Palace.