The Hammers have so far said that they will not allow the French international to re-join former club Marseille.
Payet had surprised West Ham manager Slaven Bilic by stating that his family were unhappy in London and he wanted to return to the south of France.
Marseille have reportedly seen two offers for the 29-year-old turned down by West Ham, although it is believed that they are preparing a third bid in the next hours.