The Brazilian midfielder played the final 13 minutes of Milan's 1-0 Serie A win over Udinese on Saturday as he continues his recovery from a thigh injury.
Since his return to San Siro from Real Madrid on transfer deadline day, Kaka has only made two appearances for the club, but Allegri is hopeful that he will feature in some capacity against Barca.
"I don't know if Kaka will be able to play from the beginning in the match against Barcelona," he said. "He made a good performance (against Udinese).
"Kaka is an extraordinary player.
"He has to fully recover since he had to stop for 40 days due to a muscle injury. He only played 20 minutes in a midweek match.
"When he entered the pitch (against Udinese) he increased the technical value of the team and represented a great psychological support because he entered when the team could have had more difficulties."
With Lionel Messi, Javier Mascherano and Carles Puyol all returning to full fitness last week, Barcelona will be at full strength for the Milan match. And Allegri knows his side will need to work hard to repeat the 2-0 win over the Spanish champions when the teams met in last season's competition.
"Tuesday's match is worth three points and we should try to gain them because they would almost grant us to qualify," he added. "It surely won't be easy. It will be very difficult.
"They (Barcelona) will be motivated to gain three points. I believe they may have (Lionel) Messi, (Gerard) Pique and (Javier) Mascherano, therefore the whole squad will be available.
"We have to battle and to be very careful and concentrated. It will surely be a beautiful match and we hope we'll be able to achieve a positive result."
