The appointment of Carlo Ancelotti "would be an unbelievable coup" for Everton, Jamie Carragher told Monday Night Football.
Ancelotti has reached an agreement in principle to become the next Everton manager, Sky Sports News understands, and his appointment could be announced before Wednesday's Carabao Cup quarter-final against Leicester.
Everton revealed caretaker boss Duncan Ferguson will be in charge for the visit of Brendan Rodgers' side, with the former Toffees striker set to remain as part of the first-team coaching staff, should Ancelotti be appointed.
Meanwhile, the club released a statement on Monday evening in which they said they have met a number of candidates about the vacancy, but no contract offer has been made.
Carragher, speaking on Monday Night Football, thinks the Everton fans will be ecstatic with the Italian's potential arrival at Goodison Park.
"I have to take my hat off to them if Everton pull this off," the former Liverpool defender told MNF. "The Everton fans will be ecstatic.
"I'm surprised that Carlo Ancelotti would take the Everton job with the position that they are in in the league. For Everton to get a manager of the calibre of Ancelotti would be an unbelievable coup for them.
"The supporters have been complaining a lot about managers they've had in the past and why not, rather than spending a lot of money on the pitch, give them one of the real elite managers on big-money wages, someone who's a real top football coach.
"In Ancelotti you are getting someone who is right at the top of football. This is a man who Evertonians, if it comes off, can say has won more than Jurgen Klopp and has won Champions Leagues. It gives them something to buy into with that manager."
'I'm not sure he's the man Everton need'
Ancelotti, who was sacked as Napoli manager last week, emerged as a primary target for Everton's majority shareholder Farhad Moshiri and chairman Bill Kenwright after Marco Silva's departure on December 5.
The 60-year-old won the Premier League, the FA Cup and the Community Shield during his tenure at Chelsea from 2009 until 2011 and has won league titles in four different countries.
He has lifted 15 major honours during his career, including three Champions League titles, but despite his glittering CV, Carragher has his concerns about Ancelotti being the right fit for the role at Goodison Park.
"When Farhad Moshiri came in the first manager he appointed was Ronald Koeman and he mentioned that he wanted a Hollywood manager because Liverpool had Klopp down the road, Pep Guardiola was down the road in Manchester and Jose Mourinho was at United at the time, and I loved the fact that he'd come into Everton and he was actually thinking on that level," he said.
"He wanted to get Everton back to that level so, I have no problem with Everton going for Ancelotti. But I can't change my view that I'm not sure he is the man to do the job Everton need. I think that no matter how successful Ancelotti has been in the past he's never really had this type of job or certainly excelled in this type of role
"This is a manager who has managed the top clubs in world football. The first club he had was Reggiana, who were in Serie B. That's a long time ago and you can imagine the energy and the intensity he's got to make his name in football, and it gets him those bigger jobs."
Where can Ancelotti take Everton?
"What Ancelotti does is he takes really good teams and adds a little touch to it which takes them to that next step, especially in the Champions League," he added.
"He's not going to win the league or the Champions League at Everton. That's not the job description at this moment in time and it might not be that for a long period of time, unfortunately for Everton. The job for any Everton manager is, can they get in and around the Champions League places where they are actually challenging.
"About 10 years ago Everton were in the position that Spurs were. They were both fifth or sixth, but Spurs made that jump, they got the new stadium and now they are almost recognised as a Champions League club. I think that's where Everton would like to have been, but they know how difficult that would be.
"So, the realistic target for Ancelotti is can he get them to be a consistent top six club as they were under David Moyes and could he maybe make that next step of winning a cup that Everton have gone so long without.
"The Hollywood manager they thought they were getting in Ronald Koeman, who I think is a good manager, but he didn't suit Everton. I think he just lacked the intensity that I think Everton Football Club needs and that's my one worry with Ancelotti.
"With the great career he's had, the age he's at now and coming back to a job that he's probably not done since the start of his career, that's my worry for Everton. But in terms of his CV, you'd want a man like that and rightly so. I'm sure the Evertonians are ecstatic."