Victorian and South Australian health authorities are on alert over a coronavirus case described as "particularly difficult to sort out".
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It remains unclear whether the aged care worker, who flew from Melbourne to Adelaide on Monday, is shedding the virus.
Another two positive cases in Victoria are also likely to be viral shedding, but all three remain under investigation.
Victoria on Tuesday declared its twelfth day without any new cases or coronavirus deaths.
The Department of Health and Human Services has declared hot spots at Melbourne Central and Melbourne Airport because of the aged care worker case.
Anyone who visited Melbourne Central last Sunday between 2pm and 5pm, or were at Melbourne Airport's Terminal Four from noon to 1pm on Monday are advised to be tested if they develop any symptoms.
Victorian Health Minister Martin Foley said the DHHS is working with SA authorities to formally investigate the case.
The aged care worker originally tested positive two months ago in Victoria, according to the DHHS.
She isolated and was cleared of the virus later that month.
The DHHS added the woman has not worked in aged care since October and tested positive on Monday in SA as part of her entry screening process.
She is not showing symptoms, but authorities are yet to clarify whether the woman is shedding the virus or has caught it again.
"The (expert) panel met twice yesterday - a particularly difficult case to sort out so we're treating this person as being potentially infectious for now," Victoria's Deputy Chief Health Officer Allen Cheng tweeted.
Asked how many people had tested positive to coronavirus twice in Victoria, Premier Daniel Andrews said it would be "double figures".
"It could be someone getting it for a second time, but that would be extremely rare," he said.
He added the three people were being treated as positive cases "out of an abundance of caution".
"We think that we're safe but at the same time, in all of your responses, you have to acknowledge that the margin for error is very, very small."
He also noted there had been 19,986 tests in the previous 24 hours, calling it "an amazing effort".
Other key numbers also remain steady, with four active cases in the state and one mystery case.
Two people are in hospital with neither in intensive care.
The state's virus death toll remains at 819 and the national figure is 907.
Australian Associated Press
