The transfer guru confirmed the Rossoneri coach's interest in the young Spaniard, while also adding that talks are underway to bring teenager M'Baye Niang to San Siro
This claim comes on the back of the discovery that a deal to bring former Rossoneri talisman Kaka back to Serie A would prove financially impossible, just the latest twist in a long-running saga.
The quest to sign a high-profile replacement in light of Zlatan Ibrahimovic's and Thiago Silva's departures has now led Galliani to keep an eye on Bojan, who endured a difficult first campaign at the Olimpico following his €12 million (£9.5m) loan arrival from Barcelona.
"Bojan is a player liked by Allegri," Galliani confirmed to Sky Sport 24 after revealing a return for Kaka was not plausible.
It remains unclear whether Milan will win the race to sign the Catalan youngster however, with Liga outfit Malaga touted as the favourites to secure the services of the striker.
With that in mind, Galliani alluded to a deal bringing in-demand Caen prospect M'Baye Niang to Milan, following fruitful talks with the 17-year-old's agent, Oscar Damiani.
"For the moment, Niang is a Caen player, but we'll see," the official continued. "I'm hopeful for a positive outcome."
"The boy seems a good player, which explains why we have been watching him for several years. If we sign him, he'll go into the first team, despite his tender age."