Goal understands the former Manchester City striker's representative, Mino Raiola, met with Arsene Wenger in Brazil while the veteran French coach worked as a pundit at the World Cup.
But after Wenger played down a possible move for the Italy forward, Galliani claimed that the 23-year-old will be staying at San Siro for the 2014-15 campaign.
"Balotelli will remain at Milan," he told the club's official website.
Galliani also moved to shift criticism of Balotelli's performances at the World Cup after a number of supporters believed his lacklustre showings led to the Azzurri departing the tournament at the group stages.
Balotelli began by scoring the winning goal against England in Italy's opening fixture, but he was substituted at half-time by Cesare Prandelli in his side's crucial final group match against Uruguay.
But Galliani believes there were plenty of other factors leading to the former winners being knocked out.
"It does not sit well with me that it seems that the international team has lost because of Balotelli.
"Italy lost for many other reasons. Balotelli was the only striker who has scored a goal while others have not made a shot on goal.
"I do not understand why you only talk about Balotelli. There was a coach, the technical staff and 22 other players: we have to talk about the collective.
"It seems now that the major disappointment was Balotelli.
"I do not understand this and do not want to really discuss it because I did not understand why the whole squad was not discussed."