The Ivory Coast winger left Palace last summer as a free agent, moving to Galatasaray.
However, he is not entirely happy at the Turkish giants and may want to move back to England.
Speaking to talkSPORT’s Sunday Edition, Parish said: “I’d have Wilf Zaha back in a heartbeat. He's, you know, he's part of our club, part of our history as I've said countless times.
“There's a few people that can lay claim to being at the heart of the resurgence of the club and Wilfried is certainly very much one of them.
“We've stayed in the division sometimes by the force of his will, so of course we would.
“Unfortunately it doesn't look like that's going to be possible this summer for various reasons. We continue to wish him all the best out there and I'm in contact with him every now and again.
“I'm glad to see he had a good season last season.
“He fulfilled his dreams. He played in the Champions League so it's a great story for him but of course if he was available we'd be interested.”