They returned a positive result after being tested for the virus six days after symptoms emerged on the day after they arrived home.

NSW Health and Victorian authorities declared a dozen new locations from the NSW South Coast right back to the Melbourne CBD in evening announcements on Tuesday.

The Shell service station at the Big Merino in Goulburn, as well as popular stop Trappers Bakery, are among the places listed in the public health alert in NSW.

"NSW Health has been advised by the Victoria Department of Health and Human Services [DHHS] that a confirmed case of COVID-19 from Melburne was in Jervis Bay, Goulburn, Hyams Beach and Vincentia while potentially infectious," NSW Health said.

"That person, who reported the onset of symptoms on May 25 and was tested [Monday], drove back to Melbourne on May 24."

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The traveller, who was in NSW on Sunday, May 23 and Monday, 24, arrived home prior to the southern state's lockdown and stay-at-home measures implemented on Thursday.

Anyone who was at the following NSW venues at the listed times is urged to call the state health department on 1800 943 553, get tested and isolate until further information from NSW Health is received.

A number of service stations along the Hume Highway over the Murray River are also considered exposure sites, the Victorian government said on Tuesday night.

"Investigations are still proceeding by the person has provided initial information about exposure sites," DHHS said.

Anyone who was at the following sites at the specified times are required to be tested immediately and quarantine for 14 days, the department said.

Anyone at these locations within the relevant timeframes need to get a test and isolate until a negative result is received:

More sites around Jervis Bay are expected to be added to the advisory, NSW Health said, as investigations into the case's movements are carried out. Anyone experiencing symptoms should be tested as soon as they appear, and isolate until a negative result is received.

"NSW Health is in the process of increasing testing capacity in the area, including a drive-through pop-up testing clinic in Huskisson," NSW Health said on Tuesday night, adding more information will be made available on Wednesday morning.

"Anyone who lives in Jervis Bay, or has visited Jervis Bay since May 22, is asked to be especially vigilant for the onset of even the mildest of cold-like symptoms.

"Additionally, anyone who has recently had symptoms should also get tested."

Meanwhile, a final call on the Victorian lockdown could soon be handed down after state government and health officials reportedly discussed options into the night.

COVID-19 testing commander Jeroen Weimar said there were four to five instances in the state's latest 54-case outbreak of people contracting the virus from "fleeting contact".

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