The Italian only joined Milan in January this year from Manchester City, but he is already being linked with a move.
His agent Mino Raiola has made a number of statements, which seem to confirm that Balotelli is unsettled at the San Siro.
But vice-president Galliani insists that the club are not looking to sell Balotelli, who was even linked to a reunion with his former Inter Milan boss Jose Mourinho at Chelsea.
"There is absolutely no problem with Balotelli," he is quoted by the Italian media. "Mario will continue to be our star. He is not going anywhere.
"He is a fascinating individual with global appeal.
"He will stay with Milan because he is happy here and has a long contract with the club."
AC Milan coach Massimiliano Allegri, who has stated his desire to keep Balotelli, was also discussed by Galliani, with some sections of the Italian press claiming he could be axed after an in-different start to the season.
But Galliani insists he will remain in charge until the end of the season at least.
Allegri's present deal will expire in the summer.
"Allegri will continue as coach," Galliani said. "At the end of the season we will analyse the situation as we always do.
"We are still in three competitions and all three of them can qualify you for Europe."
Following Inter Milan's decision to sell to Indonesian Erick Thohir, AC have been linked with foreign investment - but Galliani also says this is not true.
"If it were true, I would know about it and there are no on-going negotiations with regards to selling the club," he said.
"We have balanced the books and there is no need to sell the club."