Former Stoke boss Pulis has emerged as the frontrunner to take over at Selhurst Park in the wake of Ian Holloway's departure.
Parish is keen to talk to the experienced campaigner, who has never managed a club relegated from the Premier League, but he was keen to stress Palace are keeping their options open.
"We haven't contacted him (Pulis) yet but I think we will have a chat with him, definitely, if indeed he is interested," Parish told Sky Sports News.
"I don't know if he is. His name keeps being mentioned but he may be happy with whatever else he is doing.
"We've got a long list we have made, hopefully with everybody and anybody on it. We will start contacting people who are out of work and try to arrange some time to see them.
"But we will have conversations with all the usual suspects, all the obvious candidates, and maybe some not so obvious.
"We will try and make a quick decision but we will try and make a right decision."