The 21-year old defender, who has been linked with the likes of Manchester United, Newcastle United and Reading recently, is out of contract at Selhurst Park with the Eagles prepared to offload him this summer.
"We need to do a deal with Clyne,” Parish said.
"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."