Bojan, 22, arrived in Italy from Barcelona for €12 million in 2011, but failed to produce his best form during his debut season.
With Milan in the market for a striker following the sale of Zlatan Ibramimovic to Paris Saint-Germain, though, it appears that Massimiliano Allegri is eager to add the player to his squad.
"Bojan is a player Allegri likes," Galliani told Sky Sport 24 on Tuesday. "Things are moving forward. The talks are going well. Hopefully, we should complete the deal today."
It is reported that Bojan has rejected a move to Malaga in favour of Milan. The switch is expected to be a season-long loan.
Under the terms of his move to Roma, Barcelona are bound to re-sign the striker for €13 million next summer, although Roma are able to retain him should they pay €28 million.
FIFA agent Diego Tavano told SpazioMilan: "We are getting closer and closer. Milan are talking about the deal with Rome and Barcelona, who own the player's registration. I really think they can complete it quickly as Milan is a welcome destination.
"Bojan is very happy with this solution and would prefer to go to Milan rather than staying with the Giallorossi. There is still no definitive agreement, but I am confident that once there is agreement between the clubs, terms with the player will happen very quickly."
Meanwhile, Milan's hopes of signing Kaka from Real Madrid look to be over.
Galliani had earlier said the club would not sanction a permanent return for the midfielder, and on Monday he told Milan's TV station: "The tax problem? It's all true. We asked the opinion of a tax accountant who said it was 'too risky'."