The club struggled with inconsistent form in the first half of the season, leading to the departure of coach Massimiliano Allegri in January.
He was replaced by club legend Clarence Seedorf and the Dutchman's arrival has seen an upturn in fortunes, with Milan currently 10th in the table, one point shy of sixth spot, which is likely to be enough for a UEFA Europa League berth.
And Kaka wants to play a role in what he hopes will be the club's revival next season.
"I personally have done well but it hasn't been enough in the general context," he told Tika Taka.
"I can improve for next year and my intention is to stay.
"I do not even want to remain anxious and wait too long, the fans can rest easy because there are no games or anything, it will be a personal choice and that of my family, but the biggest desire is to stay."
Up next for Seedorf's side is the Milan derby against Inter on Sunday, with a trip to Atalanta and a home tie against Sassuolo also still to come.
