The Brazilian only returned to San Siro last summer after spending four years at Real Madrid, where he had fallen into obscurity alongside the likes of Xabi Alonso and Luka Modric.
Kaka's comeback season happens to have coincided with the worst Milan season in recent memory as Massimiliano Allegri was axed in January with the Rossoneri languishing in midtable while Clarence Seedorf's arrival has not heralded the instant turnaround some fans might have hoped.
Galliani, who himself has been under pressure from fan groups to step down over poor signings in recent transfer window, admitted that the 31-year-old is permitted to leave as bagging elite European football is well beyond Milan this campaign.
"It’s very simple," the club CEO told Sky Sport. "Kaka has a contract until June 30 in 2015, but if we don’t qualify for the Champions League then he has a clause allowing him to leave.
"We will discuss it, but I firmly believe he will stay."
Before Milan's clash with Chievo on Sunday, Kaka insisted that he has no plans to leave the Rossoneri in the summer by suggesting his 300th game for the club will be far from his last.
"There is always so much talk about the future," the Brazilian told the club's website. "I said I’d like to play in America, but there is time. I see myself in the Rossoneri shirt and hope to continue for a long time."