The Dutchman departed on Monday, only 77 days into a three-year contract, after Palace became the first team in England’s top division to lose their opening four league fixtures without scoring since Preston 93 years ago.
It is understood Hodgson is in talks to accept his first job in management since resigning from the England post after Euro 2016.
The 70-year-old was also approached when Sam Allardyce was appointed to succeed Alan Pardew last December, and, after a significant break from football, now looks set to return to oversee Saturday’s home match with Southampton.
Allardyce, who quit his Selhurst Park post in May, revealed on Monday evening that he had had a conversation with Eagles chairman Steve Parish regarding the vacancy.
“I spoke to Steve late this afternoon and said, for me, I wouldn’t be ready to come back,” he told Sky Sports’ Monday Night Football programme.
“I wouldn’t be comfortable at this moment in time taking a position as a football manager. I’m enjoying my life too much at this moment, watching everyone else have the weight of pressure.”
“He didn’t offer me the job but he asked, ‘What are your thoughts?’ It was a clever question. I said, ‘If you were to offer me the job at this moment in time, I wouldn’t want to go back’.”
Palace’s board had acted after losing confidence in the 47-year-old De Boer’s ability to improve results ahead of a run in which Huddersfield, Manchester City, Manchester United, and Chelsea follow Saints.
While De Boer’s time at the south London club remains longer than the shortest term for any Premier League manager - Les Reed’s 40 days at Charlton, followed by Rene Meulensteen’s 75 at Fulham - he oversaw two fewer games.
Palace produced an improved performance in Sunday’s 1-0 defeat at Burnley, whose goal was gifted to Chris Wood by an awful back-pass from Lee Chung-yong, but previous losses to Huddersfield and Swansea did little to inspire optimism. De Boer’s only victory in charge came over Championship side Ipswich, 2-1, in the Carabao Cup.
“Crystal Palace Football Club have this morning parted company with Frank de Boer.” a club statement read.
“We would like to thank Frank for his dedication and hard work during his time at the club.
“A new manager will be appointed in due course and we wish Frank the very best of luck for the future.
“There will be no further comment at this time.”
De Boer’s sacking came as no surprise to Manchester United boss Jose Mourinho, who said no manager can feel safe: “I was sacked (by Chelsea) as a champion, (former Leicester manager Claudio) Ranieri was sacked as a champion,” the Portuguese said.
“Frank de Boer is sacked after four matches and next season something incredible again, so nothing surprises me. That’s the world where we are.
“That’s the world where many of you enjoy and also contribute to the kind of pressure that managers are involved in.
“But in football nothing surprises me.”
Hodgson last worked in the Premier League with West Brom in 2012, before leaving to become England manager. A year earlier he had inspired them, as he did with Fulham in 2007/08, to secure top-flight survival.
Between his time at Fulham and West Brom, Hodgson also had an unsuccessful spell at Liverpool that lasted only six months.
Born in Croydon, Hodgson spent three years on Palace’s books as a young defender in the 1960s before leaving without making an appearance. His return would essentially bring his career full circle, in what could prove his last job.