Forest are without a home goal yet this season, and the Reds have slipped into the relegation zone with just five points from seven matches.
Sections of supporters reportedly chanted for Glasner to be sacked during the Palace defeat which ended 5-0 in the end, highlighting how close the Austrian is to being let go.
For now, the board are reportedly backing Glasner as they expect better results to come soon. However, owner Evangelos Marinakis is often ruthless when it comes to results and Jamie Carragher suggested Glasner could be near the chopping block.
“Nottingham Forest won’t get relegated I know they’re in the bottom three right now. They were really good yesterday (vs Arsenal), I watched the game.
“Even when Arsenal scored, after that Nottingham Forest had two or three really good chances and should have gotten an equaliser. They played really well at Anfield and were unlucky not to win that game.
“The only problem Glasner has is who the owner is. Now the owner is very quick to change managers, you wouldn’t be surprised if in the international break or maybe around Christmas they change manager.
“Not because Glasner has been terrible but because it almost feels like at Nottingham Forest you have to be really good as a manager to keep your job there. He’s not shy in changing it.”
The Reds fell to a third successive defeat on Sunday as they were toppled 1-0 at home to reigning Premier League champions Arsenal. They next face Ipswich Town as they seek to jump up out the relegation zone.f