Queensland police have criticised media reports that a key suspect in the murder of Cairns woman Toyah Cordingley has fled the country.

Key points: Police say speculation about the Toyah Cordingley investigation is "not helpful"

Police say speculation about the Toyah Cordingley investigation is "not helpful" Ms Cordingley's stepfather criticised the media over publishing information before the family were told

Ms Cordingley's stepfather criticised the media over publishing information before the family were told The police investigation is ongoing

Ms Cordingley, 24, was found dead on Wangetti Beach in far north Queensland in October.

Some media have reported that a male nurse who was working at a far north Queensland hospital and had been identified as a "key suspect" had fled to India shortly after Ms Cordingley was murdered.

The Queensland Police Service released a brief statement on Sunday saying the report could jeopardise the homicide investigation still underway.

"Speculation surrounding elements of the investigation are not helpful, and have the potential to jeopardise that," the statement said.

"Queensland Police Service will not be providing anything further, other than the investigation is continuing."

Family 'pissed off', says they weren't informed

News reports on Saturday revealed "potential forensic evidence" linked the Indian man to the murder scene at Wangetti Beach and that police had informed Ms Cordingley's family.

However, Ms Cordingley's stepfather Darren Gardiner criticised the media reports in a social media post on Sunday, saying the family had not been told.

Ms Cordingley's stepfather said the family were not told about the key suspect. ( Supplied: Queensland Police Service )

"Every single development in this investigation QPS have come to visit us and give us the best update they can before the information goes to media so we can be prepared," he said.

"I'm totally pissed off with how the media has conducted themselves with regards to current information and no regard for our family."

Detectives have said they believed Ms Cordingley was attacked while walking her dog on the beach on October 21.

Locals scoured the area where Ms Cordingley was found searching for clues, and days later formed a human chain and cast flowers into the ocean to "reclaim the beach".

Women who attended a Reclaim the Night rally in Cairns days after Ms Cordingley's death said the crime had hit home.