The NSW government is advising people to avoid travelling to Melbourne and Bendigo as Victoria wrestles with a coronavirus outbreak that has jumped to 15 cases.

The NSW government is advising people against travelling to Melbourne and Bendigo for the time being as Victoria deals with a fresh COVID-19 outbreak.

A COVID-19 cluster in Melbourne's north has almost doubled to 15 infections after six extra cases were confirmed on Wednesday.

"Unless you absolutely have to go down there, just consider your options," NSW Premier Gladys Berejiklian said.

Genomic sequencing shows the outbreak is linked to a Wollert man who contracted COVID-19 in South Australian quarantine earlier this month.

The man, in his 60s, could be the possible 'source case' for the City of Whittlesea outbreak, although a definitive link is yet to be established.

NSW Health Minister Brad Hazzard told reporters that as a precaution "it might be wise" to avoid Greater Melbourne and Bendigo.

Chief Health Officer Kerry Chant says those who have returned from Melbourne since May 12 should keep a close eye on the Victorian government's growing list of COVID-19 exposure sites.

They should also avoid aged care or healthcare facilities.

Anyone in NSW with respiratory symptoms should get COVID tested.

"We are dealing with an evolving situation," Dr Chant told reporters.

"We are very connected to our southern neighbours and that is why our key commitment is to make sure you address those venues of concern, recognise the situation is evolving but also, if you have the most minimum of symptoms and you have returned from Victoria, please get tested."

At least two people in NSW who visited sites on Victoria Health's exposure list had tested negative to the virus, she said.

The two people will quarantine for 14 days from their exposure date.

Ms Berejiklian said the Victorian COVID cases were a reminder of the importance of getting vaccinated.

"We're still in a very initial stage of getting our population vaccinated and that's why it's essential ... when you look around the world, look at what's happening in Victoria, that could happen in any state in Australia," she said.

"We do not have enough of our population vaccinated.

"We have greater choices for our population when the vast majority is vaccinated - that gives us freedom to make decisions."

More than 1.1 million vaccinations have been administered in NSW, including jabs overseen by the Commonwealth.

There were no locally acquired COVID-19 cases in NSW in the 24 hours to 8pm on Tuesday, with two cases in returned travellers in hotel quarantine.

NSW Health doled out a record 13,200 vaccines in the same 24-hour period.

In Greater Melbourne, home gatherings are now limited to five visitors a day and public gatherings restricted to 30 people until at least June 4.

Masks are mandatory indoors for people aged 12 and over.

The Victorian government has not yet ruled out a snap lockdown.