The Spaniard appears to be on his way out of Roma as the 2011 Serie A champions are confident of signing the attacker before the end of the day
The Rossoneri are eager to add some more depth to their attack, and head coach Massimiliano Allegri sees the 22-year-old Spaniard as the ideal signing.
Galliani met with Roma director Walter Sabatini on Tuesday morning to discuss a potential deal, and the Milan supremo believes the deal could be done by the end of the day.
"We are moving in the right direction to sign Bojan. We are confident that we can wrap up the deal today," Galliani told reporters.
Bojan came through the ranks of the Barcelona youth academy, but was sold to Roma for a fee of 12 million euros in the summer of 2011 after he failed to secure regular first team football at Camp Nou.
Barca have an obligatory clause to repurchase the attacker for 13m euros at the end of the 2012-13 campaign, but it's not yet know how his imminent move to Milan will affect this clause.