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Parish, speaking after the press conference said if he (Pulis) is interested, then Palace will talk to the former Stoke City boss.
"I don’t know Tony and I’ve not spoken to him. I don’t know whether he wants to come and manage Crystal Palace," Parish said.
"We’re second-from-bottom, it’s an attractive proposition for some and it might not be for him, I don’t know.
"There are some obvious names aren’t there? To not have a conversation with them, if they were happy to do that, would be silly.
"I’m sure we’ll contact him and if he’s interested, we’ll have a chat with him and see where we go."
Parish also confirmed the Palace board has already drawn up a long list of candidates to replace Ian Holloway.
Pulis has been installed as the early bookies favourite for the job, ahead of the likes of Neil Warnock, Roberto Di Matteo and Alan Pardew.