The Eagles are desperate to keep hold of the talented right-back but are now resigned to losing him after he turned down a new contract and Reading boss Brian McDermott is now the latest manager keen to strike a deal.
Clyne is only 21 so Palace would be entitled to compensation but the figure involved will be a lot less than the £3million the Eagles believe he is worth.
The Cottagers and West Ham are also in the running and Palace co-chairman Steve Parish says he will do all he can to get the best possible price for the youngster.
"We need to do a deal with Clyne," he revealed. "There is a bit of action in the background and we know there is a lot of interest. It is just about sorting out who it is best to go to and who will put the right money on the table. We're all working to get an outcome.
"Clubs don't want to go down the tribunal route. It is a game of cat and mouse on the fee - we've just got to let that play out."