Police in Perth have reportedly made a breakthrough in the Claremont serial killings, one of the nation's longest running investigations.

The Post newspaper has reported that police believe the person responsible for killing three women last seen in Claremont in the 1990s also raped a teenage girl in the year before the first murder.

The newspaper said police had established a forensic link showing that whoever killed Ciara Glennon in March 1997 also abducted the 17-year-old from a Claremont street in February 1995 before sexually assaulting her in Karrakatta Cemetery.

The teenager survived.

Almost one year after the sexual assault, in January 1996, 18-year-old Sarah Spiers was abducted after leaving Club Bayview in Claremont.

Ms Spiers told her friends she was tired and was going to get a taxi home, and has never been seen since.

Five months later, Jane Rimmer, 23, vanished after drinking at the Continental Hotel in Claremont.

Ms Rimmer's body was found in August 1996 in bush at Wellard, south of Perth.

Ms Glennon, 27, was the killer's third victim.

She disappeared from the Claremont area in March 1997, having also visited the Continental Hotel.

Her body was found in April of that year in bush at Eglington, north of Perth.

Police decline to comment on 'breakthrough'

Approached by the ABC, police released a statement saying they would not respond to the reported breakthrough.

"For operational reasons the Macro Taskforce has not commented on similar media reports about possible links to other crimes," a police spokesman said.

Sarah Spiers was said to be the first victim of the Claremont serial killer. ( ABC )

"Maintaining the operational integrity of this investigation is paramount if we are to bring the offender, or offenders, to justice, therefore operational outcomes must be prioritised over media and public interest.

"Media reports on an active investigation can seriously jeopardise the investigation and negatively impact future prosecutions."

Acting Assistant Commissioner Pryce Scanlan later read the prepared statement to reporters and media cameras, but would not answer questions about the case.

Premier Colin Barnett said he hoped it was the breakthrough police and the victims' families had been waiting for.

"The police have persisted in this, I don't know any more details, but I hope this does lead to further lines of investigation, because this has been a long time, 20 years now since those young girls disappeared," he said.

Post editor Bret Christian said the link would not come as a surprise.

"When the Claremont series began, we went to an ex-FBI profiler in the United States and put the four crimes to him," he told Fairfax Radio.

"And he said, 'I would be looking thoroughly at that first sexual assault. I think that's your bloke.'

"I published this and we got criticised roundly for it and publicly for publishing this opinion, which turned out to be right."

Mr Christian said as far as he knew, police had not identified the man responsible for the 1995 rape, but had re-interviewed thousands of people since originally making the link a number of years ago.

"What's really chilling is that when they [the police] began a cold-case review of the serial killings in 2004 ... they announced they would be examining the disappearance of 16 women," he said.

"So who knows how active and for how long this guy has been before this."

Investigation spans two decades

The Claremont serial killings paralysed Perth and sparked one of the biggest murder investigations in Australia's history.

Jane Rimmer's body was the first to be found, in bush in Perth's southern suburbs. ( ABC )

The Macro task force was established by police early on in an attempt to solve the mystery.

Senior officers leading the task force publicly focussed their attention on a handful of suspects, including a middle-aged public servant who lived with his parents in Cottesloe.

There have been more than 10 independent reviews of the Claremont investigation by expert crime fighters from the eastern states and around the world.

In 2008, police released previously unseen video footage of a man seen with Ms Rimmer just minutes before she disappeared.

The CCTV vision showed Ms Rimmer standing outside the Continental Hotel when a man approached her and engaged in a brief discussion.

Police said the man was the only one in the footage they had not been able to identify, but described him as a person of interest, not a suspect.

Senior officers also said in 2008 that up to 3,000 people had been investigated as part of the Macro probe.

The Macro task force remains active, two decades after Sarah Spiers disappeared.