The England international has made 27 Premier League appearances for the Gunners this term, but has fallen out of favour over the last couple of months.
It is understood that Arsenal would be prepared to sell the 27-year-old should a suitable offer arrive this summer, and according to Calciomercato, Milan want to bring the attacker to the Italian top flight.
When recently questioned on Walcott's future, Gunners boss Arsene Wenger was quoted as saying: "I don't know yet, I'm not in transfer mode at the moment, but I think he has gone through a bad spell. Let's see how well he finishes the season."
West Ham have also been linked with a move for the former Southampton youngster.