Crystal Palace announced the sacking of Alan Pardew on Thursday afternoon and are set to speak to the former England manager in the next 24 hours.
Allardyce recently said that he was ready to get back into management and said he could return before the new year.
"I think I will return probably in the new year if not before, depending on who approaches me," he told 'beIN Sports'.
"I don't think I can leave it where it ended. That is behind me now. That is a very difficult, dark period of my time but, moving on, adversity makes you stronger.
"I'm looking forward to the right place for me, whether that is in England or abroad.
"The Premier League has been a great challenge for me over many, many years and one I think I've managed to meet".
According to 'Sky Sports', a deal between the two parties is still way off, but Allardyce would most likely be interested in the position.
Palace are currently sat in 17th position in the Premier League, just one point and one place above the bottom three, and given Allardyce's record of leading teams to safety, the former England manager would be a logical choice.