Chief executive Ivan Gazidis has decided to end his time at Arsenal in September.
The 53-year-old has spent the last decade with the Gunners and was responsible for replacing long-serving manager Arsene Wenger with Unai Emery.
Sky in Italy reports that AC Milan have identified Gazidis as the man who they want to become an executive director with the club.
The approach comes at a time when Milan have recently been taken over by American hedge fund Elliot Management, and work is under way to try to move the Italian giants back up the Serie A table.
The North London outfit face further turmoil in the boardroom with reports suggesting that Alisher Usmanov is considering selling his 30% stake in Arsenal after failing to gain control from majority owner Stan Kroenke.