De Zerbi left Brighton at the end of last term ahead eventually taking the Olympique Marseille post.
Galli told La Fiera del Calcio: "On the day of his resignation from Brighton I was in his office, I was with him together with Andrea Maldera. And he wanted to come to Milan... He certainly would have come to Milan in a hurry. Then things didn't go as we wanted.
"I was there that day and he showed me photos of him from when he was at Milan, when he was in the boys' group, attached to the first team. You can feel it, when you talk to him, that he has this red and black soul, which some call Milanism."
Galli also revealed: "When I went to see him in his office in Marseille he had just finished training, but he was already totally immersed in the new reality. He has a great ability to involve everyone, from the players to the staff, but also the people who are around him and live for the club. It is clear, Marseille always has its own identity, but Roberto's passage, which I hope can be as long as possible, will certainly leave something and build a certain type of football identity if nothing else."