It is no secret the Rossoneri are looking for a long-term successor to veteran keeper Christian Abbiati, and the German shot-stopper appears to be high on their hit-list.
According to Sport Bild, the Serie A side have already been in contact with the player’s agent Gordon Stipic.
The 23-year-old has developed into one of Germany’s top goalkeepers over the years, and has also been linked with a move to Borussia M’gladbach.
Baumann, who already has 117 Bundesliga appearances to his name, has a contract until June 2018 at Mage Solar Stadion, but his release clause stands at mere €7.5 million.
AC Milan have shown a great deal of improvement under new boss Clarence Seedorf, but they face a tough task against Napoli at Stadio San Paolo at the weekend, with away win paying 11/4.