Victoria's Health Minister Martin Foley confirmed a case reported on Saturday lives in the same Southbank townhouse complex as a worker from Arcare Maidstone, who earlier contracted the virus via the aged care facility.

Authorities believe the aged care worker infected the man, aged in his 30s, in a common area of the low-rise complex, prior to testing positive.

"The epidemiology, the interviews with the two cases involved and the genomic sequencing seems to support that," Mr Foley told reporters on Monday.

"What we're trying to do is to run down the particular circumstances of that and make sure that if there are any chains of transmission out there, that we identify them early and cut them off."

The aged care worker was transferred to hotel quarantine upon testing positive.

Mr Foley said authorities are investigating two possible sites of transmission within the complex.

"As I understand it, it is not laundries," he said.

The complex has not been listed as a public exposure site.

All registered owners of the more than 100 townhouses have been contacted, while a pop-up testing facility is being established on site.

Nurses will go door-to-door to ensure people are tested.

"Most residents will simply be required to test and isolate until negative ... but a smaller number ... will most likely have to isolate for 14 days," Mr Foley said.

It comes as Victoria recorded two new local cases of COVID-19 on Monday, both of whom are children, who are close contacts of previous cases and have not been in the community while infectious.

One is linked to the Reservoir household reported last week, while the other is linked to the man who tested positive at the Southbank townhouse complex. It was previously reported by authorities that the man had a young family.

Authorities are yet to establish a link between the Reservoir family of four, who tested positive on Thursday, to the wider City of Whittlesea outbreak.

Mr Foley said contact tracers were looking at a number of cases that have contracted the virus near a Thomastown industrial precinct, just south of the Metropolitan Ring Road.

"There are as many as 10 public and private exposure sites within this particular pocket of Thomastown, with some broad overlap between a number of the positive cases," he said.

"We want to use this as an opportunity to remind everyone who was in that industrial precinct, whether you deliver goods there, whether you are part of the service delivery to that particular industrial precinct, just to think about any symptoms that you may have had."

More than 2000 Victorians are isolating after coming into contact with a positive case, while about 130 exposure sites remain listed as of Monday afternoon.

Some 16,932 Victorians were tested for COVID-19 in the 24 hours to Monday morning, while 13,764 received a vaccine dose at state-run hubs.

Mr Foley said increased testing would help authorities "run down those last few chains of transmission" left in the outbreak.

The outbreak, which began in the local government area of Whittlesea, forced Melbourne into a two-week lockdown, which ended on Friday.

The lockdown was replaced with strict restrictions, including a ban on home gatherings, a 25km travel limit and mandatory masks indoors and out, which will remain until at least June 18.

Regional Victorians are allowed two visitors at home, while density limits are in place at restaurants, pubs and cafes, gyms and other venues.

Mr Foley said the state was "on track" to further ease restrictions later in the week.

Australian Associated Press