The Frenchman has been vocal in his admiration for his young compatriot, who has forged a reputation as one of the world's finest attackers.
Leonardo reacted by accusing Zidane of destabilising the World Cup winner of destabilising the 20-year-old but the former midfielder has hit back.
"All I said was something that Kylian Mbappe had already said himself - that it was his dream to one day wear Real Madrid's white jersey," he said.
"That's all I said, and I'm saying it again today and I would repeat it again everyday. I have nothing more to say about Leonardo, I can say whatever I want."
Meanwhile Jurgen Klopp has admitted his admiration for Mbappe but insists that the sums of money involved would rule out a move to Liverpool.
Zinedine Zidane: Mbappe's dream is to play at Real Madrid
"Okay, from a sporting point of view, there are not a lot of reasons to not sign Mbappe, what a player he is.
“But it is about the money of course. No chance. Absolutely no chance, sorry for killing that story.
"I don't think there is a club in the world that can buy Kylian Mbappe from PSG. And we are involved in that too. We cannot do it, it is as easy as that.
"We have nothing to say about it to be honest, but [buying] this calibre of player is difficult."