According to Sky Sports News HQ, the London club will meet with Allardyce’s representatives in the next 24 hours for talks.
There is no agreement in place yet between Palace chairman, Steve Parish and Allardyce.
Allardyce lost the England job in September after only one game in charge.
His position became untenable, after footage emerged of him giving tips on how to get around FA transfer rules, to undercover reporters from Daily Telegraph, who posed as businessmen from a Far East firm.
But he made it clear he is keen to return to football management in the near future.