Panorama.it reports the Milanese clubs will fight each other for the Brazilian, who looks set to leave the Bernabeu with a January exit looking likely.
Reports have linked Inter with Kaka, but they have treated them with short shrift publicly.
Privately though their interest remains high and good relations with Jose Mourinho could tip the scales in their favour.
Inter remained downbeat after seeing Zlatan Ibrahimovic join Milan, and they see a Kaka move as revenge on their rivals.
Milan though are keen not to let that happen. Kaka has been frozen out by injuries, plus the arrivals of Mesut Oezil and Angel Di Maria, and has struggled to settle since his 2009 move there.
Adriano Galliani will use his strong relations with Florentino Perez to forge the apparatus of a move together.
Milan still see Kaka as a prize object and they will jump at the chance to have him back.
Mourinho is said to have told Real Madrid directors his intention to offload Kaka, and Milan have laid out a safety net to catch him. The operation will not be cheap though.
However, the Rossoneri hope to do what they did with Barcelona and Ibrahimovic.
For their part Madrid are keen on seeing Kaka's €9 million per annum wages written off from the club's expenses as retrenchment becomes the new fashion in Spain.