The Brazilian is expected to make his first appearance since agreeing a free transfer from Real Madrid in a league match away to Torino, before the Parkhead side arrive in Milan four days later.
The 31-year-old has not played in a competitive match since May 26 - although he was given a run out in a friendly for Real last Thursday - as his four-year stay in Madrid fizzled out. He acknowledged yesterday that it would take time before he is able to enjoy consistent form, but is comfortable enough to participate in Milan's group games with Celtic this season, including the return trip to Glasgow on November 26.
It is an image which might cause some Celtic supporters to wince given Kaka scored the goal which knocked the Glasgow club out at the last-16 stage of the competition in 2007. His career is perhaps in need of a similar moment to reinvigorate it, having drifted to the fringes of the squad at Real. The midfielder was reluctant to blame Jose Mourinho for his fall from grace but is none the less determined to recover his past form.
"I am definitely ready to play," said the former FIFA World Player of the Year. "I played last Thursday for Real Madrid, although that was only a friendly, but I am definitely raring to feature for Milan. Maybe it will take time to become refined on the field and gain consistency, but I am ready to play straight away.
"For the last four years I struggled to find continuity, either because of injuries or other reasons. Real Madrid was a great experience for me on a personal level. Professionally, things may have not gone how I wanted but I grew a lot and I learned a lot.
"I wouldn't say anything is Mourinho's fault. I have always taken responsibility. I am very proud to have played a part in the great history of Real Madrid, but I did lose some of the joy which comes from playing football. The first thing I am looking to do is recapture that. I think Milan is the best place for that."
Since he left Milan in 2009 players such as Thiago Silva, Alessandro Nesta, Rino Gattuso, Paolo Maldini, Clarence Seedorf and Ronaldinho have also moved on. However, Kaka is convinced the current squad at the San Siro is capable of making an impact on the Champions League this season - where they are part of a group which also comprises Ajax and Barcelona.
"I am used to a winning Milan side," he said. "I am sure Milan can do well in Italy and excel in Europe. These are winning players and they are used to dealing with pressure, as you must be with Milan - we will be fighting for titles."
Ajax might not hold such lofty ambitions in European competition this season but Nicolai Boilesen has bridled at the suggestion that the Dutch will struggle in the group stage. Prominent players Christian Eriksen and Toby Alderweireld both left the Amsterdam side during the transfer window, but their former team-mate remains convinced of the quality of the squad that remains.
"We have some big shoes to fill," said the Ajax defender, who has now returned from a thigh injury which kept him out for two years. "But we still have a strong team and our objectives are still clear: we want to get as far as possible in the Champions League and be champions of Holland once again."