Former Cagliari boss insists a player of 'important value' is likely to come in before the end of the transfer window, but he doubts a comeback for the Brazilian ace
Kaka recently said that Madrid coach Jose Mourinho wanted him to remain at the Bernabeu, but he has consistently been linked with a move back to San Siro.
Reports suggest Kaka could be among the names labelled 'Mister X' as Allegri is looking for a classy player for his side.
Liverpool's Alberto Aquilani, Fiorentina's Riccardo Montolivo and Arsenal's Cesc Fabregas have all been linked with Milan, but Kaka's arrival does not seem to fit in with the club's current plans.
"Kaka is a great player, but he currently plays for Real Madrid," Allegri told Il Corriere dello Sport. "So many players have been reported to be 'Mister X', and Kaka is just the latest. We will see.
"It's clear that if there is to be a 'Mister X' arrival then it will be an important player of value."
Speaking of Alexandre Pato, who has been tipped to join Chelsea, Allegri made it clear that there were no plans to sell him.
"Pato will stay until 2014, then we will see," concluded the coach.
Pato scored 14 goals in 19 starts for Milan in an injury-filled campaign.