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