Hodgson has done such a solid job the Eagles want to reward him by extending his Selhurst Park deal.
Palace believe Roy Hodgson has the energy, drive and success record to keep going as a top-flight manager Credit: Reuters
Palace chairman Steve Parish confirmed talks have begun.
Ex-England and Liverpool chief Hodgson, 72, replaced Frank de Boer in 2017 and has steered Palace to steady mid-table finishes.
And this season they are sixth, two points clear of Manchester United and just one adrift of Arsenal.
Despite his age, Hodgson is keen to carry on and is willing to sign a new deal.
Palace are among the teams interested in taking Rhian Brewster on loan.
GOLDEN BOOT WINNER
The Liverpool starlet is also being tracked by Swansea and Bristol City, plus clubs in Germany.
Kop boss Jurgen Klopp will weigh up whether to allow Brewster, 19, out to get regular football.
The striker has broken into the first-team so may stay at Anfield in January.
He first sprung to fame two years, helping England win the Under-17s World Cup as the tournament’s eight-goal top-scorer.
And according to Anfield assistant manager Pepijn Lijnders, Brewster could expect more first-team action this term.
Lijnders hailed “the power of the youth with experience” in Liverpool’s squad.
He added: “That mixture can bring amazing processes.”
Brewster won a professional deal at Anfield in June 2018, having spent eight years with Chelsea as a kid.