Parish dismissed former Scotland boss George Burley after the New Year's Day defeat at Millwall, with former Palace striker Dougie Freedman put in temporary control of the Selhurst Park club.
Coppell has had four spells in charge of the Eagles, and Parish said: "I don't know what Steve's situation is, whether he wants to manage or whatever. I absolutely will be giving him a ring and having a chat with him, Steve would be a great sounding board for us in terms of who we should get, he cares for the club deeply."
He added: "The word legend is used too often but in his case he's a definite legend here. He's been a fantastic manager at almost every club he's been to and he's definitely someone who I would be mad not to have a chat to.
"I don't expect Steve Coppell to apply for the manager's job at Crystal Palace, but I think it would be silly not to at least speak to him, ask him his advice or see where his head is at at the moment."
Parish was also quick to distance the club from speculation linking former Newcastle boss Chris Hughton with the vacant position after he was seen in the stands at Millwall.
"I have never met him in my life," he said. "He came to the Millwall game presumably because he was in town and he wanted to take in a game in London. That obviously set everybody talking.
"But I've not spoken to Chris, I've not had a job application from Chris, obviously he's a very good young manager so if he applies for the job we would consider it out of courtesy, but I've not spoken to him and I don't even know if he wants the job."