Milan are expected to finalise the details with Real Madrid and welcome Theo Hernandez for a medical as early as Monday afternoon.
According to Spanish site AS, the deal is practically done for €20m and the left-back will sign a five-year contract.
Another meeting is expected on Monday morning to get the final details down and he can then fly out to Italy for the medical later that day.
Theo Hernandez had also been tracked by Napoli and Bayer Leverkusen, but was convinced to join Milan by director and club legend Paolo Maldini.
The 21-year-old spent the 2018-19 season on loan at Real Sociedad, where he scored one goal with two assists in 28 competitive games.
Real Madrid spent €24m to purchase him from Atletico Madrid in 2017.
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