Pulis, who guided Stoke City to the top flight during his second spell in charge, has been out of work since leaving the Potters in May.
"I'm sure we'll try and contact him and if he's interested we'll have a chat with him and see where we go," Parish told talkSPORT when asked about his interest in Pulis.
"But I don't want to put pressure on anybody. We've started making a list, we'll throw everybody into that and see who we want to see."
Pulis and former Leeds United manager Neil Warnock have been named as the bookmakers' favourites to replace Holloway at Palace.