The Brazilian playmaker, who turned down a world record move to Manchester City in January, has not played since injuring his foot in the 1-1 home draw with bottom club Reggina on February 7.
"As soon as I manage the pain, I will return, even though I will still feel a bit of pain," Kaka told reporters. "Until last week I was not managing the pain, I hope to manage the pain better in the next few games."
Fellow attacking midfielders Ronaldinho and Clarence Seedorf also missed last Sunday's 3-0 home win over Atalanta, prompting coach Carlo Ancelotti to play two strikers instead of his preferred Christmas tree formation.
The ploy worked with evergreen forward Filippo Inzaghi, a rare starter this term, bagging a hat-trick and David Beckham enjoying a new role just behind the strikers.
Beckham, who has extended his loan from Los Angeles Galaxy until the end of the season, hopes to shake off an ankle knock to face mid-table Siena.
Kaka is also not a certain starter having been on the verge of a comeback for the last month before suffering setbacks.
Milan do not want to push him too much, especially as they will cope fine without him if they produce a similar performance to last weekend.
Critics say playing Alexandre Pato up front on his own with Kaka and Ronaldinho just behind is a tactic which has largely failed this season and is a major reason why Milan are third and 12 points behind leaders Inter Milan.
Some fans are beginning to wonder whether it might have been better to accept Manchester City's reported 100 million euro ($128 million) bid for Kaka.
Others have questioned his motivation to regain his fitness but Milan chief executive Adriano Galliani has no doubts.
"Whoever thinks he has no desire to return is crazy," he said.
Inter must recover quickly from Wednesday's Champions League elimination by Manchester United when they host fourth-placed Fiorentina, who surprisingly lost 2-0 at home to Palermo last weekend, in Sunday's late game.
Second-placed Juventus, seven behind Inter, entertain Bologna on Saturday when they will try to forget Tuesday's defeat by Chelsea.
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