Galliani was said to have made an offer for Dzeko while dining with Wolfsburg chief Dieter Hoeness last week.
But the Rossoneri supremo said: "It is not true. That is, there was dinner, we went to the restaurant simply because it was the birthday of Hoeness, who is a manager that we know from the times of Stuttgart, Hertha Berlin, now there.
"Then there was the manager of Dzeko. It was an idea of (Ariedo) Braida, I wanted to go to sleep. He told me that it was the birthday of Hoeness and I said, okay, we'll go to the birthday of Hoeness. And that's the truth, I swear."