The Chilean attacker has been struggling to make an impact at Barca and could be set for a return to Italy this summer.
The Serie A champion is keen to add some more firepower to its squad and has already secured the services of Athletic Bilbao striker Fernando Llorente on a free transfer.
The Old Lady are not done on the transfer market yet, though, and have also set their sights on the 24-year-old Sanchez.
The gifted attacker had previously already attracted the interest of Juventus back in 2011, but then opted to leave Udinese for Barcelona instead. However, Sanchez has struggled to live up to the high expectations at the Blaugrana, and has found first-team starts difficult to come by.
Therefore, he is open to a move back to Italy, where he will be allowed more tactical freedom, and the Bianconeri could launch a formal offer within a week.
Sanchez, who has a contract with Barcelona until June 2016, has netted four goals in 30 official appearances for the Catalan giants so far this term.