After missing out on Geoffrey Kondogbia the Rossoneri have set their sights on the 24-year-old.
Milan have drawn up a short list of midfielders for next season including Gündoğan, Axel Witsel and Andre Gomes.
Gündoğan’s contract with Dortmund expires next summer and the deep-lying-playmaker is expected to leave the Bundesliga in the coming weeks.
The in-demand midfielder will make a decision regarding his future “as soon as possible,” according to a statement the Dortmund midfielder published on his official Facebook page.
Gündoğan finished the season with five assists and three goals in 33 appearances in all competitions. The 24-year-old also played a staring role in Germany’s 7-0 victory over Gibraltar on last week.