The Special One has emerged as a frontrunner to take charge of the Toffees, amid rumours that new owners The Friedkin Group are considering the future of current boss Sean Dyche.
Dyche faces mounting pressure at Goodison Park, with his side sitting 16th in the Premier League table, just a point above the relegation zone, and fans growing frustrated with the team's style of play.
Ahead of Everton's FA Cup clash with Peterborough tonight, the ex-Burnley manager admitted himself that the club's owners should be looking for his replacement.
And it is now understood that TFG are doing so, with former boss David Moyes and Thomas Frank the other names linked with the job.
But Mourinho appears to be the leading candidate to take over from Dyche, despite already holding a position at Fenerbahce.
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The 61-year-old was appointed head coach of the Turkish side last summer, who are currently second in the table, despite him recently taking aim at the officiating in the league.
Should Everton make a spectacular play for Mourinho, this would be his fifth spell at a Premier League club, having previously managed Chelsea twice, as well as Manchester United and Tottenham.
And a move to Merseyside would make for a full circle moment for the Portuguese manager.
Just last year, Mourinho was handed his marching orders at Roma by TFG owner Dan Friedkin, who also owns the Serie A side.
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But there can be little doubt that the three-time Premier League champion would be keen on a return to English football.
In October, Mourinho admitted that he hoped to return to England at some point, saying: "I had three clubs in England, so four different periods I've coached in England, and I love it.
"And by the social point of view, I've been lucky enough to live in so many cities, but my family lives in London. London is home, so one day I have to be back, unless no one wants me."
Meanwhile, Dyche appears to have accepted the fact that his position at Everton is far from secure, and admitted on Tuesday that TFG were right to weigh up their future options.
When asked about speculation that the ownership are reviewing his position, he said: "It should be.
"At the end of the day, if you're a business of this size and this club, succession planning should be part of their diligence.
"I've got no problem with that at all. I think that should be ongoing at every football club. That's part of the business, surely. I'm sure it is in what we'd call normal business life, outside of football."
He continued: "I've never really concerned myself with that. We've got to win games. We haven't won enough this season. We've got to make sure the team's operating the right way.
"We've got to try and please everyone all of the time and that's the job. We haven't done that often enough and it comes down to me, without any shadow of a doubt."
And with the Toffees facing a potential banana skin in their upcoming encounter with League One Peterborough, a defeat would surely accelerate any plans for a future without Dyche at the helm.
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