The Selhurst Park club parted ways with Patrick Vieira this morning after an 11-game winless run in the Premier League.
Palace will take their time before making any decision, but under-21 coach McCarthy will take charge of their next game.
The Eagles face league leaders Arsenal on Sunday before action is paused for the international break.
Failure to impress could see the Palace board act swiftly and bring Hodgson back.
The 75-year-old left the club after retiring at the end of 2020-21.
However, he returned to the dugout briefly last season to work with Watford.
Hodgson knows Palace players and is still admired by those at the club.
With relegation starting to stare at them in the face, the Eagles cannot afford to waste any time.
McCarthy will be given the chance to make the job his until the end of the season.
However, a weak performance against Arsenal will rule him out.
Palace are also weighing up whether to bring Shaun Derry back during the international break.
The former coach was relieved of his first-team duties earlier this year by Vieira.
The Frenchman was not pleased with Derry’s man-management style.
He could return to the club as they look to get all the help they can get ahead of the run-in.
Hodgson brings plenty of experience to the table and could be the perfect short-term option.
Palace are 12th in the Premier League after a return of 27 points in as many games.
However, just three points separate them from the drop zone with 11 games remaining.
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