The pair spent 18 months together at Goodison Park in which the 24-year-old scored 20 goals across all competitions as Everton finished 12th and 10th respectively.
Sources have told ESPN Brasil that Ancelotti has told the Madrid hierarchy he would like to bring Richarlison to the club and Los Blancos will look if a deal with Everton will be possible.
Should a deal happen, it would be the second successive season the two clubs have done business with James Rodriguez having swapped Madrid for Everton last summer on a free transfer.
Madrid are unlikely to splash out on big signings this summer as they count the cost of renovating the Bernabeu, while they have also been hit financially by the coronavirus pandemic.
Though, they would be keen on a making a major signing this, but are waiting to see how much they can recoup with player sales, sources have told ESPN.