The Brazil international playmaker enjoyed a successful spell at Milan before leaving for Madrid in 2009.
However, the 31-year-old has struggled in Spain and is now seeking a move away from the club. Milan are favourites for Kaka's signature and Allegri believes that the playmaker could offer a boost to the club.
"Kaka would make the team stronger because he has great quality and is also a player we could do with. Having champions in the side is always a bonus," Allegri told reporters.
"His arrival would boost the confidence of the team and the fans. I am confident the club, Silvio Berlusconi and Adriano Galliani have every intention of keeping Milan at the top level.
"In tactical terms, Kaka could play as a trequartista in this side, or as one of the two who flow around the centre-forward."
Kaka has made 120 appearances for Real, scoring 29 goals in the process.