Hughton was at the Den on Saturday as Palace lost 3-0 to Millwall - a result that cost Burley his job.
But Parish said: "I've never met Chris Hughton in my life. He came to the Millwall game presumably because he wanted to take in a game and that set everyone off.
"I've not heard from Chris and he hasn't applied for it. But if he did then I'm sure we would consider it.
"We'd like to have a manager by the weekend. We are in the transfer window and we need fresh faces in, so the sooner the better."