Rossoneri officials were upbeat on their chances of re-signing the Brazilian yesterday morning.
Milan director Ariedo Braida fuelled talk of an imminent reunion when saying: "There is a true friendship between us and he is always in our hearts."
Nevertheless, speaking after Milan wrapped up the title at the weekend, Allegri quietened the reports.
"The return of Kaka is just a rumour," he stated on Monday. "For now we are just thinking about the present campaign.
"At the end of the season we will sit around a table and see what we can do to strengthen the team. It's too soon for that now."