Roy Hodgson is under mounting pressure after eight games without a win, with Steve Cooper in the frame to replace the Crystal Palace manager after his sacking by Nottingham Forest last week.

It is understood that Hodgson, who was seen spitting on the ground in frustration as he made his way down the tunnel after Palace conceded a late penalty to lose at Chelsea on Wednesday, is facing increasing scrutiny from the club’s chairman, Steve Parish, after the team’s plummet down the table in recent weeks. Palace are only three points clear of Luton in the relegation zone, and Rob Edwards’s side have played a game fewer.

Related: Chelsea find way past Crystal Palace thanks to Noni Madueke’s late penalty

Palace face Brentford at Selhurst Park on Saturday with Hodgson aware that his job is on the line despite his triumphant return to the club last season when he replaced Patrick Vieira after a 12-match winless run and guided Palace to 11th place. Cooper is believed to be available without having to pay compensation to Forest, with Parish having spoken to the former England Under-17 manager about taking over in the summer.

The former Wolves manager Julen Lopetegui has also been spotted at Selhurst Park in recent weeks and would be an experienced option, while the Lille manager, Paulo Fonseca, and Oliver Glasner, who has been out of work since leaving Eintracht Frankfurt in the summer, both have their supporters in the Palace boardroom.

It is understood Parish would prefer to keep Hodgson until the end of the season but is aware of the growing frustration among supporters and could be forced to act if results do not improve.

Hodgson was frustrated that VAR decided to award a penalty to Noni Madueke after he was fouled by Eberechi Eze in the 89th minute of their 2-1 loss to Chelsea but insisted he was not concerned about his position.

“It wasn’t my obvious idea of what a penalty looks like, but that’s the same for so many penalties that I’ve seen given, because I’m conditioned to some extent after seeing penalties given and not given for many years,” he said. “Then the next question is whether I’m frightened to death now because we’re only a few points above the relegation zone. I’ll answer that one for you as well: No, I’m not.”