The Egyptian team had been due to arrive on Tuesday with the initial findings of their inquiry but postponed their meeting with Italian counterparts until later in the week.
The brutal murder of the Cambridge PhD student, 27, outside Cairo earlier this year has shone a light on Egypt's human rights record.
He 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.
The Egyptian inquiry has come in for so much criticism that the editor of state newspaper al-Ahram has spoken of "naive stories" that have hurt Egypt's reputation.
"I wonder what [the Egyptian investigators] will come up with," his mother, Paola Deffendi, told a Rome press conference. She and her husband cast strong doubts on what the Egyptian authorities had said so far about the circumstances surrounding his murder.
The meeting in Rome, if it does go ahead, could be crucial in assessing whether there has been any progress. The Egyptian officials are expected to provide prosecutor Giuseppe Pignatone with evidence, such as phone taps, CCTV footage and forensic analysis, which will help the Italian team carrying out a parallel inquiry.
Cairo deputy prosecutor Mostafa Soliman and another official are due to be joined by police officers, including one from the Giza area where the young student's body was found.
The Cairo investigators have suggested that Giulio Regeni was kidnapped and killed by a criminal gang, possibly posing as members of Egyptian police.
During a raid a week ago, all five members of the alleged group were killed and some of the student's personal belongings, including his passport and some alleged personal effects, were recovered.
But that version was quickly derided by Giulio Regeni's family, who are adamant that the Egyptian security forces are behind the murder, and by Prime Minister Matteo Renzi, who said that Italy would not settle for a "convenient truth".
Giulio Regeni's death has brought international attention to the crackdown on dissent by Egyptian authorities since many believe that the murder could be linked to his research into the role of unions in the post-Mubarak era for his PhD at Cambridge University.
His wide network of international friends, colleagues from the UK academic community and Amnesty International have led a campaign to bring attention to this case in particular, as well as the issue of forced disappearances in Egypt.
For now, the family seems content with the help they have been getting from the Italian government. But they have warned that they are expecting Mr Renzi's administration to up the ante and recall its ambassador to Cairo if they are failed by the Egyptian investigators.
There have been calls, too, for the Italian foreign ministry to issue a travel advisory for Egypt, which could damage the country's already ailing tourism industry.
Giulio Regeni's parents have also suggested they might make public a photograph of their son's tortured body to increase pressure on Egyptian President Abdul Fattah al-Sisi. In an interview with Italian newspaper La Repubblica, Mr Sisi has promised to deliver the truth in the case.
Ms Deffendi, a retired elementary school teacher in northern Italy, where her son was born and raised, said last week that she had not yet been able to cry much over the death of her son.
She described in heart-wrenching detail the most gruesome details of how she recognised her son's body at a Rome mortuary.
It was the frustration about not knowing why her son had been murdered that blocked her from crying, she said. "Maybe I will, once I understand what happened to my son".
The family of murdered Italian student Giulio Regeni are waiting for Egyptian police and prosecutors to travel to Rome, in what they hope will mark a turning point in the investigation into his death.