The FIFA World Player of the Year missed Milan’s opening-day defeat by Bologna and most of the pre-season after suffering pain in his left knee, which was operated on in June.
However, the Brazilian playmaker is expected to return to competitive action this weekend after coming through the second half of a 2-0 defeat at second-division Swiss side Lugano in a friendly on Wednesday.
“I don’t feel any pain and that’s the most important thing, so I expect to be there at Genoa,” Kaka was quoted as saying by La Gazzetta dello Sport.
Milan, who finished a disappointing fifth last season, looked out of sorts after struggling in pre-season friendlies and striker Filippo Inzaghi pulled up with a thigh problem.
Also on the mend is Internazionale’s Patrick Vieira, who has made progress from a leg muscle problem and may be used by the champions against Catania at the San Siro on Saturday.
Argentina midfielder Esteban Cambiasso is one of several players who will not return until Friday from internationals in South America.
Roma captain Francesco Totti is battling to come back from an ankle knock for Saturday’s visit to Palermo, who are under new coach Davide Ballardini after Stefano Colantuono was sacked following a 3-1 defeat to Udinese.
Juventus coach Claudio Ranieri, meanwhile, should be able to call on fit-again striker David Trezeguet and midfielders Marco Marchionni and Cristiano Zanetti for Sunday’s home game against Udinese.
Inter, Juventus, Milan and Roma are all seeking their first wins of the new season.
Away fans have been banned from the Inter-Catania, Napoli-Fiorentina and Genoa-Milan games, which are considered high risk by Italian authorities.