Gattuso, banned for four European matches for head-butting Tottenham Hotspur assistant coach Joe Jordan in their Champions League last-16 tie in February, was celebrating Milan's league title triumph on Saturday when he unleashed the expletives.
The World Cup winner had been critical in the past of Leonardo's decision to join Inter in December after 13 years as a player, director and coach at bitter rivals Milan.
The usually mild-mannered Leonardo was not amused by the latest outburst.
"The day I decided to leave Milan, Gattuso said to me that I had at least been coherent in my choice. But today I read he still wants to give his own version of events," the Brazilian said in a statement issued by Inter.
"I would very much like to know what he has to say, since neither on the phone nor in person has that ever been possible."
Milan, overjoyed at finally ending Inter's five-year reign as Serie A champions, could meet Inter in the Italian Cup final if they both get through this week's semi-final second legs.
"It doesn't seem a particularly dramatic incident," Milan chief executive Adriano Galliani told reporters amid media speculation the Italian football federation may launch an inquiry into Gattuso's outburst after the 0-0 draw at AS Roma.
