The Italian club have been pitted against the Scottish champions in the group stages of this season's competition, alongside Barcelona and Ajax.
Kaka, who played against Celtic in the tournament's last 16 in 2007, has said that Neil Lennon's side will provide stern opposition.
"When we faced Celtic in 2007, they gave us two very tough games," Kaka told the Daily Record. "It was probably one of the strongest Milan sides ever with Andrea Pirlo, Paolo Maldini, Clarence Seedorf and many more but it took us until extra time to beat them.
"Celtic are such a hard working side and that is what made it so hard for us. There are only one or two left from the squad that faced them in 2007, so I'll make sure that the current squad know just how tough the two games will be, especially the one in Scotland.
"It's a hard group. We know that but we have a great squad."
Kaka recently returned to the San Siro on a free transfer from Real Madrid.