The 68-year-old has confirmed the club are in talks with Real Madrid about a possible loan deal for the former Rossoneri hero, but is maintaining a cautious approach to negotiations.
"Will it be possible to sign Kaka? It will be difficult, very difficult. How hard will I try? We’ll see...," the CEO told Sky Sport Italia.
The Brazil international spent six years in Italy before making the switch to the Spanish capital in 2009.
But he has struggled to replicate the form he enjoyed at San Siro in Spain and recently hinted he would be willing to take a pay cut to make the move happen, much to the delight of Galliani.
"It’s true, I was very, very pleased with Kaka’s words. There is contact with Real Madrid, but at the moment I haven’t got any news for you," he added.
The CEO then played down renewed speculation about a move for Mario Balotelli, following the appearance of his agent, Mino Raiola, at the club’s offices.
"[It is] a normal thing that agents come by to visit."
Milan owner Silvio Berlusconi dropped a hint that the club will make a major signing this month, with Mario Balotelli and Kaka the players he is most likely referring to.
On Thursday night told Tirreno Sat: "We're counting on youngsters now, but I think that we could make an important signing in the January transfer window."
Meanwhile, Fluminense chief Peter Siemsen has flat-out denied that they are planning to bid for the 2007 Ballon d'Or winner.
"[The deal] does not exist," he told ESPN Brasil. "You know there is a lot of speculation... but we have not even sat down to negotiate with Kaka.
"So this story does not make any sense, it was not even discussed and I do not see any possibility of happening."