The Real Madrid midfielder had been linked with a return to the San Siro after a disappointing injury-hit season.
But Galliani, CEO of the new Italian champions, said that any such deal would be too expensive for the club.
“Unfortunately Kaka will not return and the reasons are economic ones,” Galliani told La Gazzetta dello Sport.
Kaka played for Milan between 2003 and 2009 and became recognised as one of the world’s best players there, winning the Ballon d’Or in 2007.
In the summer of 2009, he joined Real for a then record transfer fee of €68.5 million, but has struggled to replicate the form he produced in Italy.
He has played 82 times for Brazil and was part of the squad that won the World Cup in 2002, also playing in 2006 and 2010 editions.
