The 20-year-old has refused a new deal at Selhurst Park, with Manchester United reportedly keen on the full-back, although Dougie Freedman believes a move could be too soon
The England Under-21 international’s current contract expires in the summer, and Palace have been unable to tie him down to the same long-term deal they agreed with fellow starlet Wilfired Zaha.
With a host of Premier League clubs – including Manchester United – reportedly interested in the full-back’s signature, Parish has conceded the player’s head has been turned and his agent is looking to broker a deal elsewhere.
He told the London Evening Standard: "Nathaniel won't sign a new contract. I have offered him a very lucrative one and I can't force him to accept it.
"His agent has got Nathaniel running his contract down - make your own mind up [what's happening]."
If Clyne departs in the summer, the Eagles will be set to receive a compensation package as the player is under 24 and has come up through the club’s youth system.
Whatever the outcome of his mooted departure, Parish is hopeful the south London side will receive a decent figure for the player’s services.
"The situation is out of our control because we didn't give him his last contract as it was before the new consortium bought the club," he continued. "The thinking before was to give him a three-year deal and then they'd be entitled to compensation.
"That is something we will have to look at as and when someone makes us an offer this month or in the summer we will expect to get a good deal on compensation. He is one of the best young players in the country and we'd expect to get something from a tribunal that would reflect that for a young player, plus all the add-ons.
"Nathaniel plays fantastically for us and we will get good money when he leaves. The way things have been done is not great but right now he is in the form of his life. He gives 150 per cent for us and if he sees out his contract, there is not much more you can ask for."
Parish admits that promotion is the only way in which Clyne is likely to stay with the club, adding: "If we were to get into the Premier League this season it may make a difference because that is where he wants to play."
Palace boss Dougie Freedman believes the 20-year-old would be making a mistake by leaving, suggesting he is not yet ready for the step up to top flight.
He said: "I've told him I don't think he is ready and I strongly believe under my coaching he will get better, which he has shown this year. He needs to be careful he doesn't jump too quickly. But he seems to think he is ready, which is fine, I understand that. That's his privilege to have that opinion."