A South West Healthcare spokeswoman said the hospital was unaware of specifics of the case and referred The Standard to the Department of Health and Human Services.

Other Warrnambool-based health services that have conducted testing would not reveal whether any patient had returned a positive result for coronavirus, citing confidentiality.

The department said they wouldn't provide details about individual cases unless necessary in the interests of public health.

"As part of our contact tracing, relevant public exposure sites are contacted and provided with advice about the transmission risks and any cleaning that may be required," a department spokesman said.

"Anyone who tests positive for coronavirus, whether or not they have symptoms, must immediately self-isolate and will be contacted by a public health worker from the department for advice on next steps.

"There are strict procedures in place to protect the public wherever someone tests positive to coronavirus, including close contacts being identified and notified that they need to self-isolate and seek testing."

The department linked a case to Warrnambool on Sunday, the first connected to the city in more than 14 weeks.

On Monday Victoria recorded 177 new coronavirus cases. Twenty-five of those cases were linked to contained outbreaks, one was in hotel quarantine and authorities were investigating 151 cases. There were 1612 active cases statewide.

Victoria's Chief Health Officer Brett Sutton said despite the number being lower than Sunday's 277 cases, he was "not going to be complacent".

"It's great that it is lower than our peak, but it might not be our peak yet. I would want to see a week of decreasing numbers before I had comfort about the direction we are going in," he said.

Premier Daniel Andrews said the disease was a "clever, complex, cunning, clever enemy that we're all fighting".

"We can get there if we stay the course and acknowledge all of us have a really important part to play in that," Mr Andrews said.

Medical professionals conducted 22,943 tests on Sunday, bringing the state to more than 1.1 million tests.

"Please keep coming forward to get tested if you even have the mildest symptoms," Mr Andrews said.

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