The report suggests that current Crystal Palace boss Alan Pardew is under pressure.
The current Eagles boss Alan Pardew is coming under increasing pressure at Selhurst Park, according to the Mirror, and the board are already making plans for if they decide that they need to make a change.
Allardyce - who has been out of work since his departure from England - is one of the names in the frame, and the Mirror reports that he would be interested in considering the job with Palace, despite their current position.
Crystal Palace manager Alan Pardew
Crystal Palace have lost their last six games in the league, including a hugely disappointing and incredibly dramatic 5-4 defeat away at potential relegation rivals Swansea City in their most recent fixture.
That form has left them above the bottom three only on goal difference. And with a crucial run of games ahead - they face the likes of Manchester United, Chelsea and Arsenal as well as the side directly below them, Hull City in their next six - it is surely imperative that they turn the form book on its head if they want their situation to look a lot brighter after the hectic Christmas period.
Should their situation become even bleaker however, it would perhaps not be a surprise if the board looked at the work that Big Sam did at Sunderland last season and considered him to be the best man to get them out of trouble.