Diame arrived at Upton Park on a free transfer from Wigan Athletic in the summer, but reports suggest that there is a £6 million clause in his contract that would allow him to leave the club if a club came in for him.
The Frenchman has put in some fantastic performances for the Hammers this campaign and the London club are trying to get him to sign a new deal before January to avoid a team signing him so cheaply.
Liverpool and Everton are both monitoring the situation of Diame and he may be tempted by a move to Merseyside.
His performance in West Ham’s 3-1 win over Chelsea over the weekend earned him a lot of plaudits with some pundits comparing him to Manchester City star man Yaya Toure.
Sam Allardyce knows that when a player puts in displays like this then they will always attract the attention of other English Premier League teams and will be concerned with the current contract that the former Wigan man has.
With under a month to go until the January window opens, the Hammers need to act quickly.