According to La Gazzetta dello Sport (h/t Sport Witness), the Rossoneri are prioritising free transfers this summer and "contacts are continuing" with the Gunners star, as they see him as a player who fits the bill.
Corriere dello Sport (h/t Sport Witness) added Wilshere impressed Milan boss Gennaro Gattuso when he helped Arsenal overcome the Italian side 5-1 on aggregate in the round of 16, and his performance "convinced him he could play a role" at the San Siro.
Wilshere's contract is up in the summer and he is yet to agree on a new deal. Per Indy Football, Gunners boss Arsene Wenger is hoping he'll stay but has given little reassurance he will:
Meanwhile, Gattuso was vocal in his praise of Wilshere after his side came up against the England international in the Europa League, per Mark Mann-Bryans of the Press Association:
The 26-year-old's career at the Emirates Stadium has been severely hampered by injury problems and further absences will be a risk for any side that pursues him this summer.
He has returned to the Arsenal side this season after breaking his leg while on loan with Bournemouth last year, though, notching two goals and five assists in 31 appearances.
While his fitness has often been an issue in his career, his talent has never been in doubt; his ability to drive the ball forward and carve open a defence with an incisive ball make him a valuable asset.
Despite concerns over his ability to stay fit for long periods, he could be worth a gamble as a free transfer given what he can offer on the pitch.