Greenwood has moved to Marseille from Manchester United after being named Player of the Year while on-loan with Getafe.
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The forward rebuilt his career in Spain after assault charges were dropped against him in January.
De Zerbi told L'Equipe: "Greenwood is the first player I called. I spoke with his father, who must be the same age as me.
"I warned him about the demands of this club, telling him: 'Marseille is Marseille'.
"He replied: 'I remember the historic Marseille which played in European Cup finals'."
De Zerbi also said: "I said that when a player becomes my player, I am the first to pin him to the wall when he makes a mistake.
"But towards the outside, I will always defend him as I would defend my son."