Tuttosport says Milan moved for the 23 year-old after being convinced of his fitness in recent months under coach Davide Ballardini.
Milan want to sign Canini on an initial loan, with concerns remaining over his previous knee injury. In exchange, Cagliari will receive the full ownership of Alessandro Matri, plus Ignazio Abate, currently on-loan at Empoli and Davide Astori, now at Cremonese.