Brazilian coach asks Rossoneri to explain outburst against him as club are furious with heated comments
Gattuso was seen celebrating Milan's Scudetto win at Roma with fans when he started to sing what have been described as anti-Leonardo chants.
The Italian FA have opened a probe into the allegations. Gattuso reportedly chanted: "Leonardo man of s***."
Leonardo, who is preparing for the Coppa Italia semi-final, second-leg against Roma tomorrow, has invited the Italian midfielder to explain his motives.
"Gattuso, on the day I decided to leave Milan, came to me and said at least I was coherent in my choice," Leonardo told Inter's official website.
"I read in many papers today that he still wants to speak about the truth. I would like to know what he still needs to say, seeing that on the phone or in person, it was never possible.
"I would also like to know Milan's stance on what has happened."
Nerazzurri president Massimo Moratti is less than impressed with Gattuso.
"Leonardo was very sad at what happened. He is not happy. But I will not judge. This incident closes itself," said the chief.
Milan CEO Adriano Galliani has been quick to respond though. He told Sky Sport Italia: "I have not seen the video. But I think it's just a pity. Players are like that, let's not make a drama."