Seventy-three-year-old Hodgson's contract is due to expire at the end of this season, and Lampard is among Eddie Howe and Burnley's Sean Dyche on Palace's wish list to take the reins at Selhurst Park.
Chelsea legend Lampard was dismissed of his duties at Stamford Bridge at the end of January, having managed the Blues since the beginning of the 2019-20 campaign.
The Burnley boss and ex-Bournemouth manager have both held talks with Palace, and the club are expected to hold talks with Lampard about the possibility of taking over from Hodgson.
Lampard guided the Blues to a fourth-placed finish in his first season in charge, despite having to work with a transfer ban over the club. body check tags ::