The officials at Cairo airport said Giampaolo Cantini arrived on a flight from Rome.
An Italian embassy official could not confirm Giampaolo Cantini had landed in Cairo but said the envoy should "arrive today".
Italy has rejected multiple theories suggested by Egyptian investigators, including a road accident, a botched crime or a personal vendetta, and always insisted those responsible be found and brought to justice.
The Italian press and western diplomats in Egypt suspect members of Egypt's security services of having abducted, and fatally tortured Regeni, a 28-year-old doctoral student who was writing about trade unions in the country.
An Italian autopsy showed Regeni's body was covered with cuts and his bones were broken, indicating he had been hit with "fists, batons and hammers".
Egyptian officials today said police had arrested a lawyer whose human rights group opposes enforced disappearances and is linked to the defence of Regeni's family.
Ibrahim Metwally was detained on Sunday at Cairo airport on his way to the Swiss city of Geneva, where he was to take part in a meeting on enforced disappearances, his group said.
Prosecution officials said he had been remanded in custody for two weeks on suspicion of "dealing with foreign parties" and "spreading false news".