Help us find suspects behind Giulio Regini's murder: family
"We know who they are, what their faces look like, and we know how much harm they are capable of doing. Will you help us look for them?" the Regeni family's lawyer said in a Facebook post.
A trial of the four in absentia in Rome was thrown out by judges in October because prosecutors were unable to prove they had managed to inform the defendants of the judicial process against them.
The officers stand accused of kidnapping, conspiracy to murder and grievous bodily harm in the case, which sparked outrage in Italy and has strained diplomatic relations with Egypt.
"We need their residential addresses so we can try them in Italy. Help us to find them. Let's not give them the chance to... continue to do all the evil in the world with impunity," lawyer Alessandra Ballerini wrote.
"Anyone who has news about them and their home addresses please contact me. I will protect the anonymity of any witnesses," she said, posting photographs of three of the four men.
The 28-year-old Regeni was doing research for a doctorate at Cambridge University when he was abducted in Cairo in January 2016.
His body, bearing extensive signs of torture, was eventually found dumped on the outskirts of Cairo, naked from the waist down.
The Italian government joined the proceedings with a civil suit for damages, in a symbolic show of support.
But the trial juddered to a halt before it could begin when the court said it was not possible to be certain that the four suspects, members of Egypt's National Security Agency (NSA), were aware of the proceedings against them.
Egypt has repeatedly refused to provide their contact details.
The four are named in court documents as General Tariq Sabir, Colonels Athar Kamel and Uhsam Helmi and Major Magdi Ibrahim Abdelal Sharif, who is accused of carrying out the killing.
Investigators believe Regeni was abducted and killed after being mistaken for a foreign spy.