The health department on Thursday confirmed genomic testing is underway on another two cases, in the cities of Brimbank and Wyndham, who returned results with the S gene dropout, a signature of the new variant.

Four potential Omicron cases are now under investigation.

At least three cases are not linked to international travel and the acquisition source remains unknown.

Workers and travellers through Melbourne Airport have also been put on notice after two wastewater detections showed traces of the Omicron variant on December 1 and 2.

The positive samples, from two airport catchments, are "consistent" with a known suspected case who visited the airport.

It comes after Victoria on Wednesday recorded its first Omicron case among an international traveller from the Netherlands who arrived in Melbourne on December 3 and went directly into hotel quarantine.

Premier Daniel Andrews has reiterated the state is not chasing an "Omicron zero strategy", describing it as unachievable and not the "smart thing to do".

"This thing is in our country and will be more widespread than any surveillance will show you," he told reporters on Thursday.

"That's just the nature of this virus. There's always more cases than you know about."

While health experts are trying to learn more about the variant since it was observed in South Africa, Mr Andrews noted early evidence suggested it was milder than the Delta strain and current vaccines are not compromised.

The premier has received no health advice to reimpose some restrictions to quell an Omicron outbreak, akin to those announced in the United Kingdom.

"They're having to have conversations about lockdowns and conversations about all sorts of things because they're at 60 or 65 per cent double dose, not 95 per cent double dose," he said.

Some 91.8 per cent of Victorians 12 and over are now fully vaccinated and daily COVID-19 cases remain steady in the 1000s with hospitalisations in the low 300s.

The state reported another 1232 new infections - its fourth day in a row of four-figure cases - and a further nine deaths on Thursday.

Meanwhile, an attendee at Sunday's Liberal Party state council meeting at the Melbourne Convention and Exhibition Centre has tested positive for COVID-19.

In an email to members on Wednesday night, Victorian party director Sam McQuestin confirmed the case and said the health department deemed the event a "lower risk exposure scenario" and, as such, attendees should monitor for symptoms.

Federal Treasurer Josh Frydenberg and Victorian Opposition Leader Matthew Guy were among the hundreds of members at the meeting.

It is understood the COVID-positive attendee was seated towards the back of the event and had no contact with MPs, with the main risk of exposure in the registration area.

Australian Associated Press