Ancelotti managed Real from 2013 to 2015, leading them to the 10th European Cup triumph against Atletico Madrid in Lisbon in 2014.
Now the 61-year-old is set for a second spell after Zinedine Zidane's own second tenure came to an end last week.
The Daily Mail says West Ham boss Moyes, who managed the Toffees for 11 years, is in the picture to replace Ancelotti at Goodison Park, alongside former Wolves manager Nuno Espirito Santo and ex-Bournemouth boss Eddie Howe.
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