The Independent has been told that the Spanish club are confident that the deal will happen, while many Goodison Park players now expect a change of manager in the summer.
Madrid moved quickly on Monday night after the departure of Zinedine Zidane, and contact was made through intermediaries. Ancelotti is said to be open to the possibility of returning, despite ruling out the prospect earlier this season.
President Florentino Perez sees the Italian - who won the Champions League with Madrid in 2014 - as one of the few coaches who understand the unique context of the Bernabeu job, even though there is an increasing belief that Europe's most successful club actually need a wholesale revolution.
Zidane was scathing of the running of the club in an open letter to media explaining his departure.
Everton would want "a big name" to rival Ancelotti if the Italian leaves, although the names currently put forward are Nuno Espirito Santo, David Moyes, Eddie Howe and Graham Potter.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies