The Mirror says Palace are understood to have been alerted to Pardew's interest by an intermediary.
Palace chairman Steve Parish has publicly stated that he would prefer to hire a manager with links to the club.
Pardew, 52, played 130 games for the club and famously scored the last-minute goal that beat Liverpool in the 1990 FA Cup semi-finals.
He still has a house in Surrey and is thought to be weighing up the pros and cons of leaving the Geordies, who were knocked out of the League Cup on Wednesday by Manchester City.
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