The Telegraph claim Milan are preparing an offer worth €3m for Olivier Giroud, but Italian sources insist he must leave Chelsea for free.
The striker has been in negotiations with the Rossoneri for weeks and a two-year deal was reportedly close to an agreement.
However, Chelsea then announced last week that they had activated the unilateral option to extend his contract back in April.
His agents have assured Milan and the Italian media that there is a promise to let him leave for free if an offer from abroad comes in.
According to The Telegraph newspaper, Milan are ready to offer €3m to resolve the issue.
Instead, most Italian sources including Sky Sport Italia, Sportitalia and Tuttomercatoweb warn the Rossoneri will look elsewhere if they can’t get the veteran on a free transfer.
The forward turns 35 in September and was on target twice in last night’s France friendly win over Bulgaria.