While Glasner's outburst after defeat to Sunderland on Saturday left directors dismayed, they have refused to move to sack the Austrian.
The Daily Mail says the key influence has been chairman Simon Parish, who has argued Glasner deserves a better farewell than a controversial dismissal given what he has achieved with the club.
There has been an argument raised that Glasner was deliberately pushing the board to dump him after claiming he had been "abandoned" by the board after the sale of Marc Guehi.
However, Glasner hasn't been shy criticising management publicly over decisions he disagrees with.
Palace are winless from their past 10 games, which included the FA Cup holders being knocked out by non-league Mansfield.
