Zenga says he would like to train former club Inter, but not for the time being as Mourinho is the No 1 in the world.
"Zenga is a friend, but tomorrow he will be an 'enemy' for 90 minutes," Mourinho said.
"Walter is great. He studies the opponents very well. We don't know how Palermo will play, so we will be prepared for everything."
Asked if Zenga is his natural heir, Mourinho replied: "I don't know if I decide that, but I would like it a lot. Zenga is a great friend of my great friend, so he is my friend. It's my philosophy of life.
"His career as a coach is 'anti' to the usual one of great players. He has travelled the world just to arrive at a coaching position in Serie A: the United States, Romania, Yugoslavia. I respect him a lot for this.
"Tomorrow, Zenga will play at his home. When I played in my city and in the club of my heart, 20m from my house and 50m from that of my parents, I wanted to win at all costs.
"For Walter it will be different. He will be received in a splendid manner by Inter fans and then he'll be an enemy for 90 minutes."