A lawyer in Rome, representing accused Easey Street killer Perry Kouroumblis, has told the ABC the 65-year-old will not fight extradition to Australia.

The Australian-Greek national was detained by Italian authorities on an Interpol Red Notice last week that flagged him as being wanted by Victorian police on charges of murder and rape.

The bodies of Suzanne Armstrong, 27, and Susan Bartlett, 28, were found in their Collingwood home in January 1977, when neighbours heard Ms Armstrong's 16-month-old toddler crying in his cot.

They had been stabbed in what police described as a frenzied attack.

Police said Ms Armstrong was sexually assaulted and stabbed, while it is believed Ms Bartlett was stabbed after she heard the disturbance and went to the aid of her friend.

A member of the Armstrong family said they were in "disbelief" and appreciated the "tireless work from Victoria Police and the Italian authorities".

"We know that there is still a long road ahead, but we are so grateful that the accused has chosen to cooperate with authorities at this point."

The family member said they hoped the development would assist in bringing "Suzanne and Susan's story to a close". 

Mr Kouroumblis was 17 at the time of the women's deaths, living with his parents near the Easey Street terrace house and attending the school where Ms Bartlett was a teacher.

He was stopped by police in the week following the women's deaths near Easey Street, telling officers he'd found the knife that officers uncovered in the boot of his car.

Mr Kouroumblis moved to Greece in 2017, telling friends he had to go to look after his sick mother.

Lawyer, Serena Tucci, said Mr Kouroumblis has told authorities he will cooperate with the extradition.

"Perry exercised his right to remain silent, said he was innocent and gave his consent for extradition," Ms Tucci said.

She said Victorian authorities have 45 days from the date of his apprehension to prepare an extradition application.

Detectives from the Homicide Squad were expected to travel to Rome from Melbourne as part of that process.

A date is yet to be set for Mr Kouroumblis to face an extradition hearing.

Victoria Police Chief Commissioner Shane Patton had described the Easey Street deaths as the state's most serious and longest cold case to reach an arrest.

The case was notorious for the way the women died and the decades of police work, prompting the head of Interpol, Jurgen Stock, to post to X upon Mr Kouroumblis's apprehension.