Parish says Palace have received numerous applications to succeed Dougie Freedman, who left the Eagles to take over at Bolton last week.
But bookies favourite Coppell is top of his list of potential candidates Parish wants to speak with.
"He (Coppell) is in a job at the moment, but he has such a history with the club and we will look to have a chat with him," Parish told the Croydon Advertiser. "We don't know what he might or might not want to do.
"It is a great job for somebody. We've got to turn a negative into a positive and like with everything in life, it is an opportunity for someone else.
"The phone hasn't stopped ringing. Palace is a very attractive proposition. It is easy to lose sight of that, but it is a great job at the moment."