Gazzetta dello Sport says a breakthrough in negotiations has been struck and there's now a confidence that Gazidis will make the move to Italy.
Milan had been pushing for an answer from Gazidis this month.
Indeed, talks are now at an advanced stage over a salary for Gazidis. The offer will be worth almost double what he earns at Arsenal.
He will arrive to take the pressure off new president Paolo Scaroni, who wants to step back from the day-to-day running.