In the closest anyone at Milan has to come to saying the Brazilian is leaving, Galliani told Thursday's Gazzetta dello Sport that the club had little option.
"The reasons for the departure of Kaka are solely economic," he said. "Even a great heart must confront the situation and make choices. Milan cannot go on losing 70 million euro a year."
Galliani has long bemoaned generous Spanish tax laws that make it very difficult for Italian clubs to compete with their La Liga counterparts in the transfer market.
Milan owner Silvio Berlusconi, the Italian prime minister, has not sanctioned any move yet and has said he will talk to Kaka on Monday before making a decision.
Hundreds of Milan fans gathered outside the club's city centre offices on Thursday to protest against the possible sale.
Banners included one which read: "If you sell Kaka, sell the club".
Media reports had said the Dubai ruler Sheikh Mohammed bin Rashid al-Maktoum was interested in investing in the club but Milan and sources in Dubai have rejected the stories.
Chelsea, coached by former Milan boss Carlo Ancelotti, denied on Wednesday that they had bid for Kaka.
Reports have also linked the Premier League club with Milan's Alexandre Pato and Andrea Pirlo, but Galliani was adamant they were not leaving.
"We're not falling apart. The other big players are not for sale. Now a great attacker will arrive," he said.
Milan have long been interested in Arsenal striker Emmanuel Adebayor.
Kaka, the 2007 world player of the year, was linked with Manchester City in January for a world record fee in excess of 100 million euro, far more than Real are reported to have offered.
"In January, Kaka didn't want to go to Manchester City," Galliani added. "Instead he would go to Madrid."
