Palace have failed to pick up a point or even score a goal in their four league games under De Boer, becoming the first top-flight team since 1924 to start the season with four defeats and no goals.
The Dutchman only took over at Selhurst Park in June, but the club's dismal start to the season has left his job hanging by a thread already and the Palace hierarchy are reportedly looking at possible replacements.
Hodgson - who has been out of work since being sacked by England following their ignominious exit from Euro 2016 last summer - currently tops that list, while David Moyes and Chris Coleman have also been linked.
Moyes was sacked by Sunderland following their relegation from the Premier League last season, while Coleman has previously hinted at a return to club management - although he is currently in the middle of a World Cup qualifying campaign with Wales.
De Boer lasted just 85 days in his most recent role at Inter Milan.