Benitez is widely expected to sign a new deal at Newcastle, but Murphy believes that the Spaniard is stalling over his future - in the hope that a better offer comes along.
With Everton on the hunt for a new manager, Murphy sees Benitez as a possible candidate to take over at Goodison Park.
He said: “I do [think he’s stalling]. I can’t say I blame him. I’m going to put it out there. I have a feeling he could end up at Everton.”
Another candidate who has been talked about as a potential new manager of Everton is Stoke City boss Mark Hughes.
Hughes has done an impressive job at the Britannia Stadium since taking over from Tony Pulis, and he is becoming an in-demand manager.
However, Murphy believes that Hughes will stay with Stoke in the belief that he can continue to take them forward.
“I think he’ll stay at Stoke for one more year,” the former Fulham midfielder added. “If he’s allowed to go again in the market, I think he’ll stay.”
Despite Murphy’s prediction, Benitez does not feature as one of the front runners to land the Everton job.
The likes of Unai Emery, Manuel Pellegrini and Frank De Boer are believed to be more likely candidates to take over at Everton.