The Cambridge student's murder outside Cairo earlier this year has shone a light on Egypt's human rights record.
Egyptian police and prosecutors are expected to share initial findings of their investigation, which has faced strong Italian criticism.
Regeni, 28, disappeared on his way to meet a friend on 25 January.
His body, mutilated and showing signs of torture, was found in a ditch on 3 February.
Giulio Regeni murder: Family in Italy expects Egypt answers
Body of Italian student found in Egypt
The BBC's Julian Miglierini in Rome says the case has strained the relationship between Egypt and Italy, and expectations for the meeting in Rome on Thursday morning are running high.
Our correspondent says that there is a feeling in Italy that the Egyptian authorities are not moving fast enough in their investigation into the murder.
His family and the Italian government have been unsatisfied by the several contradicting accounts given by the Egyptian authorities of what may have happened to the Cambridge University student after he went missing.
Prime Minister Matteo Renzi has said Italy would not settle for what he called a "convenient truth".
"We owe that to Giulio, his friends, his mother, father, his little sister - and we owe it to all of us. We hope and we think Egypt can co-operate with our magistrates."
Many in Italy think that Regeni could have been targeted by the Egyptian intelligence services because of his research on trade unions and activism.
But Cairo investigators have suggested that he was kidnapped and killed by a criminal gang, possibly posing as members of Egyptian police.
At the meeting in Rome, Egyptian investigators are expected to deliver evidence such as phone taps, CCTV footage and forensic analyses which could help the Italian team carrying out a parallel inquiry.
Regeni's mother, Paola Deffendi, recently told a Rome news conference that she and her husband had strong doubts about what the Egyptian authorities had said so far about the circumstances surrounding his murder.
Cairo deputy prosecutor Mostafa Soliman and another official are on Thursday due to be joined by police officers, including one from the Giza area where the young student's body was found.
Regeni, 28, disappeared on 25 January, the fifth anniversary of the uprising against President Hosni Mubarak, while there was a heavy police presence in Cairo.
His body was found a week later in a ditch on the outskirts of Cairo, showing signs of severe torture.
Egypt's initial autopsy report said Regeni had been hit on the back of the head with a sharp instrument.
Much of the evidence of torture came to light in a second autopsy by Italian doctors. Italy's Interior Minister Angelino Alfano said Mr Regeni had suffered "something inhuman".
As a PhD student at the University of Cambridge, Regeni was carrying out research on trade unions and labour rights in Egypt, a sensitive topic in recent years.
Rumours about possible involvement of Egypt's security services in the killing have been reported by the Italian press, activists and opposition groups.
Cairo investigators have suggested that Mr Regeni was kidnapped and killed by a criminal gang posing as members of Egyptian police.
Police then said they had killed all five members of the alleged gang in a raid and recovered some of Mr Regeni's personal belongings.
Mr Regeni's family say they are adamant their son was killed by Egyptian authorities and that the criminal gang theory is a cover up.
Egyptian officials are briefing Italian counterparts in Rome on the progress of an investigation into the torture and murder of student Giulio Regeni.