The Eagles sacked Patrick Vieira in March after they went through a 12 match winless run amid worries about relegation.
The Crystal Palace hierarchy re-appointed the experienced Hodgson as their manager to guide them back to safety.
Under Hodgson, the Eagles saw a remarkable turnaround in form and picked up 17 points from nine games to ensure their Premier League status.
There has been speculation regarding the new Palace boss for next season and former Chelsea boss Graham Potter has been linked with the job.
However, it has been claimed that Crystal Palace are waiting to hear Hodgson’s decision regarding whether he wants to stay at the club before shortlisting candidates for the job, due to respect for the boss.
It has been suggested that the London outfit are interested in keeping Hodgson at the helm for next season.
Crystal Palace have one more game left in their season and the 75-year-old tactician will be focused on finishing the season on a strong note.