The 25-year-old has impressed at Upton Park since completing a free transfer from Wigan Athletic after running down his contract at the DW Stadium.
Senegal international Diame is reportedly attracting attention from a number of clubs and a release clause exists in his contract.
Hammers co-chairman David Gold confirmed the fact on Twitter, as he said: "Diame does have a release clause in his three-year contract. He joined us from Wigan on a free transfer."
West Ham boss Sam Allardyce would not be drawn on the speculation regarding the finer details of Diame's agreement but did admit a big offer would leave the club "powerless".
"I don't disclose players' contracts publicly. There's always a situation where you're powerless to keep a player because of the size of the price," he said.
"You can't turn it down. The chairman says, 'Look, we can't turn that down, Sam - we've got to move him on'."