The 22-year-old scored twice in Everton’s 2-1 victory over Newcastle at St James’ Park on Saturday as the Toffees made it two wins from two under Ancelotti.
Calvert-Lewin also netted the Boxing Day winner against Burnley, and is the club’s leading scorer this term with eight league goals in 18 games.
And Ancelotti has seen enough from the young striker to predict he will go on to great things.
The Italian, who has managed the likes of Cristiano Ronaldo and Zlatan Ibrahimovic, said: “He is a fantastic striker in my opinion – fantastic with the head, clever in the box, and sharp.
“But he’s young and for this reason he has to improve. He is a humble guy and he doesn’t talk a lot.
“I think he is going to be at the top in England and in Europe. He has all the qualities to be a top striker.”
Despite the positive start to his tenure, Ancelotti has already begun to pinpoint the improvements he believes his side can make as they look to secure their place in the top half of the table.
“We had difficulties in the second part of the first half where we suffered a lot and lost control of the game,” added Ancelotti.