The 20-year-old's current contract expires in the summer and he has so far refused Palace's offers of fresh terms.
"Nathaniel won't sign a new contract. I have offered him a very lucrative one and I can't force him to accept it," Parish told the London Evening Standard.
"His agent has got Nathaniel running his contract down. Make your own mind up [what's happening]."
Clyne made his Palace debut in October 2008.