The Merseyside-based club are three points off the relegation zone after an abysmal start to the season led to the departure of manager Marco Silva.
Duncan Ferguson’s appointment as interim head coach has somewhat steadied the ship, taking four points out of his first two games, nevertheless a permanent appointment is set to be made at Goodison Park.
Ancelotti has reached an agreement in principle to become the next Everton head coach according to media reports, although the Toffees released a statement on Monday evening distancing themselves from contacting the former Chelsea manager.
Carragher insists the Toffees fans will be very elated if Everton appoint a manager of Ancelotti’s standard.
"I have to take my hat off to them if Everton pull this off, the Everton fans will be ecstatic” the 41-year-old told MNF.
"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."
