Barely 72 hours after his appointment, Tare made a move for Allegri, with a three-year contract being added to the former Rossonero coach.
Allegri was out last season after his controversial resignation in the aftermath of a passionate Coppa Italia celebration with Juventus.
Tare, TMW reports, has decided that Sergio Concukicao should be moved and replaced by a more experienced Serie A coach.
After initially making an attempt for Antonio Conte in Napoli, the Albanian now focused on Allegri with the Milan board, convinced that their offer will be accepted.