The defender's current deal is due to expire in June.
But the London Evening Standard reports the 34-year-old's contract is to be extended. Initial talks have already taken place.
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But that's not all - Palace will also retain six other senior players whose contracts expire in a few weeks.
These include Jeffrey Schlupp (31) and Will Hughes (29), who have each played 31 competitive matches this season. Glasner has been in charge at the London club since February this year.