Nicknamed "Diabolik", the 55-year-old has evaded arrest for 24 years and is wanted for a string of crimes including dozens of murders.
Possible hideouts in "grottoes, caverns or even bunkers inside buildings" where he may be concealed are being searched in and around Castelvetrano, his Sicilian hometown, La Repubblica reported.
According to the newspaper, it has been suggested that he may have fled the country and is in hiding abroad, only returning to Sicily from time to time.
Two years ago, police discovered he had been spurning modern technology to communicate with mobsters.
Instead he was using the age-old method of "pizzini", bits of paper containing messages, left under a rock at a farm in Sicily.
Known for his ruthlessness, he also had a reputation as a womanising playboy with a love of flashy cars.
Despite being on the run since 1993, he is thought to have succeeded notorious godfather Toto Riina, who died last month.
Riina, one of Sicily's most notorious Mafia bosses, was nicknamed The Beast during his time in charge of Cosa Nostra because of his ruthless cruelty.
Among the most brutal killings he ordered was of a 13-year-old boy who was kidnapped to stop his father telling Mafia secrets. The teenager was strangled and dissolved in acid.
The latest blitz is being carried out by officers from the Italian capital Rome, as well as Palermo and Trapani in Sicily.
It is the second one in as many weeks by the authorities on the the real-life Sicilian crime syndicate depicted in the Godfather movies.
Last week, a woman suspected of masterminding a reshuffle of the crime group after Rina's death was arrested by police.
Maria Angela Di Trapini is accused of filling in for her jailed husband, Salvatore Madonia, working her way up from being a lowly messenger to the boss.