According to The Sun, Ferguson had the chance to follow the Italian to the Bernabeu after he quit Goodison Park last week.
But Big Dunc, who is a legend on the blue half of Merseyside after making 273 appearances for the club, turned down the approach in the hope of succeeding Ancelotti in the Toffees’ hotseat.
Ferguson, 49, believes his ready to have a go as permanent manager after a spell as caretaker in 2019.
The Scot stepped in two years ago following the departure of Marco Silva and picked up five points from three matches.
He started his temporary spell in charge with a 3-1 win over Chelsea before back-to-back draws against Man Utd and Arsenal.
Although Ferguson may want the job on a permanent basis, he is not the bookmakers’ favourite.
Former Wolves manager Nuno Espirito Santo is the man tipped to take over at Goodison Park.
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Ex-Everton boss David Moyes is also in the frame having so far failed to agree an extension to his current deal with West Ham.
Ancelotti, meanwhile, has already begun work in his second spell at Real Madrid.
The 61-year-old is keen to sort the futures of several first team stars, including Gareth Bale, Raphael Varane and Sergio Ramos.
He still had time to send a parting message to Everton fans, though, tweeting: “I would like to thank Everton, my players and the supporters for giving me the opportunity to manage this fantastic and historical club.
“I decided to leave as I have a new challenge with a team that was always in my heart, Real Madrid.
“I leave taking with me all the amazing moments we have experienced together and wish the club and fans all the best.”