"I don't know what Steve's situation is," said Parish.
"I will be 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."
Coppell, who has had four spells as Palace boss, watched their 1-0 win over Preston on Monday.
The 55-year-old left his role as Bristol City boss in August, just two games into the new season following a three-month spell.
"The word legend is used too often but in his case he's a definite legend here," added Parish. "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.
If Steve Coppell gets the nod his first home game would be against Bristol City! Funny old world
Hilareious
"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."
Meanwhile Parish has played down speculation linking Chris Hughton with the Eagles.
"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."
Source: BBC Sport
Source: BBC Sport