The French centre-back has not played since November after limping out of a league clash against Real Sociedad with a knee injury.
However, the 20-year-old could make his return this weekend against Athletic Bilbao at San Mames.
"He's training and he's fine. He could be in the squad on Sunday," Ancelotti told reporters at a press conference.
Varane appeared 33 times for Los Blancos last season.