Major General Khaled Shalaby was sentenced to one year in prison in 2003 for complicity in the abduction, torture, and murder of an Egyptian man identified as Shawqy Abdel Aal.
The police chief has already claimed that Regeni - who was found with cigarette burns and repeated stab wounds - had in fact been killed in a tragic accident, and denied the existence of other injuries on the body.
An Italian autopsy on the body, found in a ditch on the side of a desert road, revealed that the doctoral student suffered "inhuman, animal-like" violence.
Egyptian officials have denied the findings.
"We are still waiting for the forensics authority's report to show whether [the victim] was tortured," said Egypt's interior minister Abdel-Ghaffar this week.
|Photo gallery: Egyptians mourn for Giulio Regeni outside the Italian embassy in Cairo|
On Friday, two suspects were arrested for the death, though they have not yet been identified.
Meanwhile, it emerged on Thursday that Italian officials contacted Egyptian authorities just hours after Regeni disappeared in central Cairo last month, according to an official summary of Italian efforts to locate him.
The summary, obtained by The Associated Press on Thursday, says Ambassador Maurizio Massari contacted Italian intelligence agents, who reached out to their Egyptian counterparts shortly after Giulio Regeni disappeared on January 25, the anniversary of Egypt's revolution.
Regeni, a 28-year-old Cambridge University PhD candidate who had been carrying out research focused on workers and labour rights - a sensitive topic, since disgruntled workers were among the forces of the 2011 anti-Mubarak uprising - and authorities still worry about worker discontent.
Regeni's disappearance came at a time when Egyptian officials and media have often depicted foreigners as plotting against Egypt - and particularly as seeking to foment unrest surrounding the January 25 anniversary.
In the lead-up to the revolution anniversary, Egyptian security forces had been searching thousands of apartments in downtown Cairo, particularly focusing on foreign residents of the area.
Italian media in particular have honed in on the hypothesis that elements in Egypt's security forces, which have been repeatedly criticised by human rights watchdogs, had arrested the young man because he was in contact with Egyptian labour activists as part of his research.
Ghaffar, the interior minister, said Egypt was treating the case "as if it were a case involving an Egyptian" - a statement that provoked scorn, due to the frequently scant investigations into Egyptian deaths.
Agencies contributed to this report