The Italian took charge of OM over the summer after leaving Brighton.
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L'Equipe says before the opening game of the season, De Zerbi used a projector at a team meeting to show the contract tabled by United.
It's claimed he told the players: "This is where I could have been, but I put my passion before money. I came to Marseille for the passion."
De Zerbi is under contract with Marseille until June 2027.
He has threatened to quit OM after Friday's home defeat to Auxerre.