Discussions with Partizan Belgrade continued after negotiations during the winter market, when the Serbian club was asking for at least €10m.
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Now, the Rossoneri are aiming to lower the price to €5m plus bonuses for the youngster, who has already scored eight times in 21 first-team appearances.
Kostic was recommended to Milan in the summer by Rossonero legend Savicevic.
Milan sports chief Igli Tare is pushing to settle on a deal with Partizan well before the market reopens this summer. In their favour is Kostic's eagerness to see the move happen.