The 62-year-old has been out of work since losing the England coaching job in September, just 67 days after he was hired by the Football Association.
Allardyce, who oversaw just one game in charge of the national side, was dismissed after being secretly filmed by undercover reporters from The Telegraph appearing to discuss how to get around the FA's ban on third-party ownership of players.
According to The Mirror, the former West Ham United boss has told friends that he is keen to return to management, and would be willing to listen to a potential offer from the Eagles.
It is believed that the London outfit would consider Allardyce, and they have already made contingency plans in the event that Pardew is booted out of the club, but no approaches have been made as yet.
Pardew has witnessed his team suffer six defeats on the trot - a run that has not befallen Palace since November 2013.
The club currently sit 17th in the Premier League table, just one place above the relegation zone on goal difference.