De Zerbi recently withdrew Greenwood from his starting XI, but denies claims of a rift with the former Manchester United forward.
He told L'Equipe: "Greenwood is a natural talent, thanks to his mother and father. I am here to help him become more complete. When he needs a hug or a few supportive words, I will gladly give it to him. When I need to be on him to give more, I will do it. That is my job.
"Above all, I want to help him be remembered, in this stadium and by these fans, as one of the best to ever play at the Stade Vélodrome. There have been so many great players here, but I think Greenwood can be remembered like that. I'm trying to help him reach that level."
De Zerbi also said: "He's had a bit of a hard time lately when his daughter was born and I don't think he's used to playing this intensely and being one of the key players. He had to pay the price for it physically.
"That's why he didn't give his all and wasn't 100 percent the way I wanted in training. I expect more from a player like that. If a player doesn't give his all in training and can't do it in a match either, it's only right that he be benched."