The Brazilian, who succeeded Carlo Ancelotti last May when the Italian left for Chelsea, has stayed silent on the issue in order to concentrate on the Serie A run-in but chief executive Adriano Galliani has admitted the rookie may quit.
"He has three kids in Rio and sooner or later he will go back to Brazil," Galliani told Sky TV this month.
Italian media speculated on Thursday that club owner Silvio Berlusconi had decided to sack Leonardo in any case after reports said the Italian prime minister had been overheard discussing Milan's average season and possible new managers.
Milan have not commented on the speculation, just as they refused to confirm Ancelotti's departure for Chelsea until the end of last season despite talks having gone on for months.
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.
