The report suggests that both the Hammers and Crystal Palace have made the Senegal international an offer for next season.
Fenerbahce are also thought to be interested in securing the services of Diame, who is out of contract at current club Newcastle United in the summer.
The 32-year-old lost his place in the Magpies side at the turn of the year to youngster Sean Longstaff and it doesn’t appear the powerful midfielder will be offered a new deal in the summer to remain at St James’ Park.
Diame, who has plied his trade in England since 2009, has made 97 league appearances for Newcastle during his three-year stay, and the midfielder could well continue his stay in the Premier League with the Hammers next season.
Diame's West Ham career in numbers
Diame made a total of 77 appearances during his three-year stay with the club. 71 came in the league, with the remaining six in domestic cup competitions.
The midfielder scored seven goals for the club, all of which came in the Premier League.
The energetic midfielder only received seven bookings for the Hammers, one every 11 games.
Diame featured in the 2012 Olympic Games and the Africa Cup of Nations for Senegal during his time in London.