The 31-year-old last week admitted he wanted to leave the Santiago Bernabeu after four years - having joined from Milan for a reported 70million euros (£56million) in 2009 - and Rossoneri chief Galliani has moved quickly to try and bring the Ballon d'Or winner back to Serie A.
Kaka is set to sign a reported two-year contract with Milan - on greatly reduced terms - while Real president Florentino Perez is not asking for financial compensation, according to the Gazzetta dello Sport.
Speaking to reporters from the Italian newspaper outside Madrid's Bernabeu stadium, Galliani said:
"There is an agreement with Real for Kaka."
"He hasn't signed with Milan, therefore he is not a Milan player."
Kaka won the Champions League and one Scudetto during his six years in Milan and lifted the Primera Division trophy with Real in 2012.
But when speaking after scoring twice for Madrid in Thursday's 4-0 win over Deportivo La Coruna in the Trofeo Teresa Herrera, Kaka said in AS: "I want to go.
"I think now is the right time for me and for the club to leave amicably. I've spoken with (Madrid coach Carlo) Ancelotti and with the club, they all know.
"My father is talking now with the club to try and resolve this situation.
"Things are now difficult for me in the team and the club know what I want. It's my obligation to work hard and continue training, but my father is already working to see if something comes up. I think that it's best for me and for the club."
Kaka has also scored 29 goals in 87 appearances for Brazil and has represented the Selecao at three World Cups.