Premier Mark McGowan says the man in his 30s returned a "very weak" positive test result in recent days but has since tested negative.

He is in isolation and has not displayed any symptoms, having previously tested positive to the virus in March last year after returning from overseas.

The man worked as a maintenance contractor at Fortescue Metal Group's Cloudbreak mine in the Pilbara between July 20 and July 27 and went on to attend venues in Fremantle, Scarborough and Subiaco.

He is believed to have contracted the virus at Perth Airport from a Queensland man who flew there on July 20 and was subsequently denied entry to WA. That man tested positive to the Alpha variant of the virus upon returning to Brisbane.

"It's a highly unusual situation," the premier told reporters.

"The best explanation we have for his weak positive test result is that he probably acquired it from the man at the airport through some sort of casual contact.

"We think he was positive over the course of the last 16 days ... (but) there's a strong prospect he wasn't infectious because he was COVID-positive early last year."

Health Minister Roger Cook said WA Health would update a list of six exposure sites, including the airport, as new information emerged.

Anyone who attended those sites must get tested immediately and quarantine until they return a negative result.

"There will be a large pool of casual contacts," Mr Cook said.

"There's no reason to believe this will lead to a lockdown but there's very much cause for concern."

The FIFO worker's girlfriend has tested negative, as has one of his three closest workmates. Results are pending for a flatmate and two other co-workers, one of whom is described as currently being in a remote location.

All are being treated as close contacts and must quarantine for 14 days.

The infected man, who had been tested while in Perth under Fortescue protocols, is awaiting the results of further testing.

Fortescue said in a statement it was working closely with WA Health to assist with contact tracing.

"In accordance with the directions of the Department of Health, all team members who were on site during that period are not required to isolate unless they are identified as a close contact through contact tracing," the company said.

"Fortescue has a comprehensive COVID-19 management plan and protocols, as well as access to rapid antigen testing on site."

It's understood Fortescue shares contractors with at least one other neighbouring Pilbara miner, which is deep-cleaning items as a precaution.

The Australian Nurses Federation said it would postpone a planned rally on Thursday at Perth's King Edward Memorial Hospital.

More than 400 nurses had been expected to protest over staff shortages and working conditions at the state's primary maternity hospital.

ANF state secretary Mark Olson said the government should take precautionary measures including restricting crowds at the AFL on the weekend.

"COVID will come into WA, it's just a matter of time," he said.

"We must protect our hospital system and hospital workers with full force now ... or we will have a disaster worse than NSW."

Australian Associated Press