"He is currently regarded as a reinfection of coronavirus," Mr Andrews said. "It is through an abundance of caution that we are assuming that is a positive case, rather than the person shedding after the original infection."
There have been a small number of reports globally of people contracting the novel coronavirus more than once, but none so far recorded in Australia. Mr Andrews said a number of experts had analysed the tests of the potential reinfection case and had been unable to determine whether it was remnants of an old infection or a new positive case.
"If that is the case, then that will be one of only a handful of those sorts of reinfection cases we have seen anywhere in the world," he said.
A day earlier, the Premier said the state was "well placed" to bring forward the easing of further restrictions planned for 2 November. This would include the reopening of all retail and hospitality businesses in Melbourne.
On Wednesday, he reiterated that he hoped to be able to announce the further easing of restrictions on the coming Sunday, including potential changes to the number of people allowed at religious services.
The low case numbers come as the government backflipped on a decision to allow more than a thousand people attend Melbourne's Cox Plate horse race this weekend, igniting widespread backlash.
Mr Andrews said he had supported the original decision to allow stakeholders to attend the race, which had been signed off by the state's public health team, but conceded it was the "wrong decision".
"We shouldn't have made that decision, we did, but now that decision has been changed and it will not be occurring on Saturday," he said.
New South Wales recorded two new locally-transmitted cases in the 24 hours to 8pm on Tuesday.
People in Australia must stay at least 1.5 metres away from others. Check your jurisdiction's restrictions on gathering limits. If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
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Please check the relevant guidelines for your state or territory: NSW, Victoria, Queensland, Western Australia, South Australia, Northern Territory, ACT, Tasmania.