Atletico Madrid, Juventus and Tottenham also want the Italian Euro 2020 star.
The Italian forward has entered the final year of his contract but is reportedly demanding higher wages in order to pen an extension.
However, Napoli president De Laurentiis is unhappy with Insigne’s standoff and willing to let him go this summer if a suitable offer arrives.
Currently, in his prime years and after serving the Partenopei for around a decade, Insigne could be seeking a new challenge elsewhere.
Atletico Madrid, Juventus, Tottenham and Barcelona are understood to have registered their interest in Insigne, but reports state that Rossoneri is leading the race.
Milan are working on attacking reinforcements ahead of the new season where they will play in the Champions League, and Insigne, who is valued at €30m, has been cited as a great option.
The Partenopei skipper is coming off an impressive 20/21 season where he racked up 19 goals and 10 assists in Serie A, followed by an excellent run in the Euro 2020, helping Italy to lift the title. He scored one of the best goals of the tournament in the quarter-finals against Belgium.
Rossoneri have been linked with quite a few names in the ongoing summer transfer window, having recently captured Olivier Giroud from Chelsea.
Insigne can be a fruitful addition to Stefano Pioli’s side, and besides his experience, his flexibility to play as a winger and a No.10 would be an added advantage.