Even though the Eagles made a decent early start to their season they have faced multiple rocky results recently.
The Selhurst Park outfit have won only one of their last five league matches and on Wednesday night they were beaten by Bournemouth.
The Cherries won the match 2-0 at Selhurst Park, with Palace fans making their feelings clear and Hodgson appearing to do himself no favours by suggesting they have been spoiled of late.
Hodgson is under pressure and it has been claimed that another Premier League manager would be looked upon favourably by Crystal Palace.
Cooper, who is under pressure himself at Nottingham Forest, has big backers at Crystal Palace, where he is admired.
Hodgson has six months left on his current contract at the south London club and he will be looking to stay at Selhurst Park until the end of the season.
Now it remains to be seen if the Crystal Palace hierarchy will make a decision on Hodgson if the Tricky Trees sack Cooper in the coming weeks of the season.