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.
Assistant coach Filippo Galli is seen as favourite by bookmakers.
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.
Most Rossoneri fans were underwhelmed by the appointment of former technical director Leonardo, seeing the move as a cheap way of finding a new coach amid general belt-tightening from Berlusconi which included the sale of Kaka and limited new buys.
Milan have not won the scudetto since 2004 and lie a distant third in Serie A with three matches to go, just four points above in-form Sampdoria who threaten to steal the third automatic Champions League spot.
Fiorentina visit the San Siro on Saturday in a tricky clash.
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.
The sight of treble-chasing Inter Milan and coach Jose Mourinho dancing with delight in Barcelona on Wednesday having reached the Champions League final will also have brought home to Berlusconi how far his 2007 European Cup winners have fallen.
