Scottish giants Celtic are also looking to lure him to Celtic Park.
The vastly experienced midfielder is out of contract in the summer and the Hoops are interested in signing him on a pre-contract.
Several Premier League clubs feel that he could be a reliable option in midfield as a free agent.
Championship outfit AFC Bournemouth are also looking to add him to the squad next summer.
McCarthy would be a very good signing for the Hammers. The 42-times capped international has a wealth of Premier League experience, and he still has plenty to offer at the top level.
He has enjoyed a good career, managing over 100 appearances for both Wigan Athletic and Everton. However, he has managed only eight appearances this season for Palace, and it seems he is heading out of Selhurst Park this summer.