Ancelotti re-joined Real Madrid on Tuesday in a shock departure as the Italian replaced Zinedine Zidane.
The Toffees are now tasked with finding a suitable replacement with the club at a critical juncture.
Everton are coming off a disappointing season while also pressing ahead with plans to build a new stadium.
Journalist Steve Hothersall believes it makes a lot of sense to appoint Benitez.
"Ever since he returned from China, he's been scouring world football for that next opportunity," he told talkSPORT Drive.
"He wants to stay in the Premier League and there aren't many clubs that actually fit the bill for him.
"Some might say Everton doesn't because he infamously said something about them being a small club.
"I think he would crawl over hot coals to manage Everton. It's on his doorstep, there's a man who owns the football club who is clearly very wealthy and could fund his ambitions.
"He'd probably have big project laid out for him and Rafa would love it."
Benitez is vastly experienced having won league titles, cups, the Champions League and Europa League.
He spent six years in Merseyside where he led Liverpool to Champions League and FA Cup glory.
The Spaniard still lives in the area and Liverpool legend Jamie Carragher urged Everton to seriously consider hiring him.
"As Carlo Ancelotti returns to Real Madrid, Everton owner Farhad Moshiri will be wondering when he will next get the chance to appoint a former Real Madrid manager and Champions League winner with Premier League experience," Carragher wrote in The Telegraph.
"How about immediately?
"Of the names instantly linked with Everton as the Ancelotti news broke, who is more qualified than my former Liverpool boss Rafa Benitez?
"Rafa is available, settled in the area and I am sure he is ready if Moshiri is prepared to consider one of the more shocking managerial appointments in Merseyside football history.
At the very least, Benitez should be under consideration as Moshiri begins yet another managerial quest. And not for the first time, before the owner decides the right candidate, he has to be clear of the football direction he wants to take."
Carragher added: "With Ancelotti, Everton pursued the tried-and-tested, proven experienced manager and stellar name. If that is what Moshiri still wants, Benitez is an obvious candidate."
WIN £50,000 with Dream Team Euros
The best fantasy football game to accompany Euro 2020 has arrived.
And you can play absolutely FREE for your chance to win the £50,000 jackpot.
CLICK HERE TO SIGN UP FOR FREE!
Dream Team Euros
£50,000 jackpot
The best fantasy football game this summer
Play in mini-leagues against your mates, colleagues, family members - and some hand-picked celebrities
FREE to play