It has been claimed that the Italian wants the striker out but he has apparently already spoken with the player about leading the Rossoneri next season
ANSA claimed on Tuesday that Rossoneri boss Massimiliano Allegri had raised the issue of offloading the striker with owner Silvio Berlusconi, claiming that the pair's relationship had completely broken down and that this season's Capocannoniere had become a divisive influence in the dressing room.
However, Milan quickly dismissed that report and, according to Tuttosport, Ibrahimovic remains very highly regarded by Galliani, who allegedly asked the player 10 days ago if he would consider the captaincy for next season.
With current skipper Massimo Ambrosini set to leave the club when his contract expires this summer, the position will soon be vacant.
Thiago Silva is still considered the frontrunner for the role but Galliani is willing to hand the captain's armband to Ibrahimovic in an attempt to persuade the Sweden international to remain at San Siro.
Ibrahimovic has only been at the club for two seasons, having initially joined on loan from Barcelona in 2010 before making the deal permanent the following summer.