Media reports said the Italian prime minister had been overheard by senators discussing Milan's poor tactics, average season and possible new managers, with assistant coach Filippo Galli seen as favourite by bookmakers.
"I don't know what Berlusconi said but I can't deny that our relationship is difficult. We are very different, maybe we are incompatible but the important thing is these next three games," Leonardo told a news conference on Friday.
Galliani then laughed off the reports about Berlusconi's comments but Leonardo, increasingly tetchy in front of the media in recent months, was clearly not amused.
"It's an incompatibility in terms of style," added Leonardo, querying why Berlusconi had not publically denied the reported comments and refuting speculation he will succeed Brazil boss Dunga after the World Cup.
"I can say that I have never talked with anyone at Flamengo or the Brazilian national team, or the organisers of the 2014 World Cup (in Brazil)," said the coach, whose length of contract at Milan has been shrouded in secrecy.
"I don't have any real offers from anyone and I'm not even thinking about it."
Milan's campaign started badly and a pickup in form mid-season, highlighted by a win at Real Madrid, soon dropped off as they bowed out of Europe and injuries to the likes of Alexandre Pato and David Beckham hit their progress.
