The former Manchester United forward has been outstanding for OM this season - both in Ligue 1 and in the Champions League.
Ahead of Sunday's blockbuster with AS Monaco, which will see Greenwood reunited with his former United teammate Paul Pogba, De Zerbi was full of praise for the England cap.
"I see him every day, he has huge potential," the 46-year-old said. "I don't see any other players in Europe at the same level. He has the potential to win the Ballon d'Or. It will be up to him to decide whether he wants to do everything he can to fight for it or not.
"At the level of the qualities that nature has given him, that his parents have given him, I think he is worthy of the Ballon d'Or.
"I would like him to be more consistent. I know he needs to press with more intensity, he needs to manage the ball better when the team is in trouble, not lose the ball easily but keep it to allow the team to move up because he has the ability to do it."
De Zerbi, however, still wants more from the winger.
"The important thing is that he understands it in three or four years," he added. "Not necessarily now, when I no longer train. When he remembers me, he will say, 'Ah, it was the coach who really took my head every day but maybe in the end I managed to progress'.
"I have to leave Marseille in a better situation than when I arrived. Greenwood must be better than the Greenwood I took at the beginning."