Clyne’s contract with Palace is set to expire in the summer and the defender has recently been linked with a move to Manchester United.
“We’ve offered him a new contract, an improved one,” Palace boss Dougie Freedman told the South London Press.
“We’re still trying to keep in line with the current wage structure and we’re just waiting for Nathaniel to come back to us.
“I think he’s progressing and should stay a little longer, he is getting better. He needs to be careful he doesn’t jump ship too early but that is his choice.”