The pressure is mounting on Pardew following a poor 2016, which leaves them with the worst points tally for the entire Premier League during the calendar year.
Palace sit just above the drop zone following another defeat against Swansea at the weekend, and unless results improve quickly, he could be heading for the exit door.
The Eagles hierarchy are already considering possible replacements, which includes former England boss Roy Hodgson and current Wales boss Chris Coleman.
Allardyce is also said to be on the list of possibilities and reports claim he would jump at the opportunity to return to club management with Palace, following his ill-fated short spell in charge of England.
Big Sam has proven on several occasions that he has what it takes to drag clubs out of trouble and he could get the call again if Palace decide to axe Pardew.