The Dutchman, 23, has shown glimpses of brilliance since moving to Lyon in January 2017.
Last month, he hit a sensational last-minute winner as Lyon beat runaway leaders Paris Saint-Germain 2-1.
Gazzetta dello Sport says his form has alerted the Rossoneri, who are interested in signing someone who can play on the left wing.
Milan have had success recently in improving the careers of wingers who have struggled in the Premier League.
Despite spending around £200million in the summer, former Liverpool man Suso remains arguably their best player.