In the official daily numbers to 8pm Monday, there were just three new cases linked to the Avalon cluster, found amid just over 16,000 tests.

However, Ms Berejiklian said there was growing concern about the threat to Greater Sydney and regional areas.

"The threat in Greater Sydney is almost becoming as equal to parts of the Northern Beaches and that's where we'll be adjusting potentially some of our restrictions," she said.

"Until those links are established, all of us in Greater Sydney have to be on high alert."

She said the Wollongong case and a two others - one from the Inner West and one in the northern area of Sydney - had come in very late overnight or early on Tuesday morning and may be eventually linked to the Northern Beaches.

The Wollongong case had visited Sydney, Ms Berejiklian said.

NSW Chief Health Officer Dr Kerry Chant said it was believed the Wollongong case "had spent some time in central business district, but ... it's premature."

She said NSW Health wanted to release the information about the three extra cases as the low official numbers had been "reassuring".

"This highlights how the situation can change quite rapidly," she said, adding that interviews about which venues or transport links the new cases may have visited were "occurring now".

The possible exposed venues list was expected to be updated later today, she said.

She also said she wanted to testing rates to rise back up to the 30,000 mark, and urged people to take extra care over New Year's Eve.

In the past 24 hours, the state continued to add a number of Sydney venues to its COVID-19 alert list, including David Jones city store, Coles supermarket in Edgecliff, Bondi beach Woolworths, Uniqlo in Pitt Street mall, several buses around Bondi, and north shore line train services.

A full list of venues and public transport routes, and the associated public health advice, is available from the NSW Government website at https://www.nsw.gov.au/covid-19/latest-news-and-updates.