The Brazil midfielder - who played for the Rossoneri between 2003 to 2009 - returned to San Siro on a free transfer last week after four years with Real Madrid.
He played 45 minutes in a 4-0 friendly win against Chiasso of Switzerland on Saturday, wearing the captain's armband, and showed enough to suggest he could be a key player for Allegri this season.
"Kaka has great quality, is a champion and his presence raises the level of self-confidence throughout the squad," Allegri told Milan Channel. "I must do well to get the best out of him and help him reach peak fitness. You cannot expect a player, even one of his level, to be ready straight away.
"Kaka is a lovely guy who is eager to work hard, which he proved already in training."
Kaka's arrival could prompt a change in formation, with Allegri likely to be tempted to opt for a system that allows the Brazilian freedom to play behind the strikers.
"We have to work, as we changed our tactical system with forwards who allow me to vary my options," he added.
"I am happy because we have almost everyone available."