The Austrian has a contract at Selhurst Park to 2026 and has just guided Palace to the FA Cup semifinals.
Glasner's impact has brought him to the attention of bigger clubs, with RB Leipzig targeting the former Eintracht Frankfurt coach.
Red Bull football chief Jurgen Klopp wants to bring Glasner back to Germany after the dismissal of Marco Rose on Sunday. RBL sacked Rose and replaced him with Zsolt Low, who has been appointed to the end of the season.
Glasner is Klopp's priority target, but talkSPORT says talks over a new deal have now commenced with Palace.
Palace chairman Steve Parish is driving the deal and spoke with Glasner last month to kickoff negotiations.
The Palace manager rejected an offer from Bayern Munich at the end of last season and has intimated he is happy in London with the Eagles.