More than 15,000 swabs were still to be processed as of last night and today's test results will be key to knowing whether the outbreak has been contained.
However, the Government still has no evidence of how the infectious UK variant B.1.1.7 made its way in to the country.
No new community cases were recorded on Monday or Tuesday.
Ministers will meet at 3pm, before Prime Minister Jacinda Ardern is scheduled to deliver the Government's decision at 4.30pm.
Cabinet will be examining a number of key issues, such as the all-important Papatoetoe High School test results and from where exactly the latest community outbreak, involving a husband, wife and daughter, came.
The later meeting time means ministers will have examined the most up-to-date information on the latest community outbreak and experts' advice.
Mr Hipkins told RNZ's Morning Report programme today he hadn't been informed of any more cases overnight - which was "probably a good sign".
"No evidence of community spread so far, and that's a really positive sign. We've managed to identify and isolate and test close contacts for the three cases and again that's a good sign, it means that we can contain any spread from there.
"So far their results are coming back negative, which suggests that if they have passed the virus on it won't have spread any further because we've managed to isolate their close contacts.
"Even if they do subsequently get it, the odds of them spreading it to anyone else are very, very low."
Hipkins said the outbreak was taking a different course than the Auckland August cold store cluster, which led to a two-and-a-half week lockdown.
In testing after that outbreak, cases came to light within a day or two, but there hadn't been anything similar this time, he said.
"Those are good contributors to Cabinet's decision this afternoon. There are still some question marks that we'll want to have as much information around as we can, including more information on the source investigation."
There are a variety of "highly unlikely scenarios" that the government is looking at to determine how these cases happened "and it has to be one of the highly unlikely scenarios".
One one expert is calling for the Government to place Auckland into Level 2.5, rather than pulling the alert level back down to 1 or 2.
University of Otago epidemiologist Prof Michael Baker was optimistic about the numbers yesterday but warned that Auckland was not ready to go straight down to Level 1 or 2.
Rather, reinstating Level 2.5 would allow Auckland to largely reopen for business, while continuing restrictions aimed at disrupting the potential Covid chain of transmission.
Today's decision will be strongly influenced by what Covid-19 Response Minister Chris Hipkins has described as the ‘‘last pieces of the puzzle’’.
On Sunday night, Ms Ardern said Auckland would remain at Level 3 until at least midnight tonight and the rest of the country at Level 2 over the same period of time.
Before Ms Ardern's announcement today, the focus will be on the Ministry of Health's Covid-19 update, where Director-general of health Dr Ashley Bloomfield will reveal if there are any new cases in the community.
No new community cases have been identified since the initial three were discovered on Sunday — heartening results after a community testing blitz in Auckland.
Although this was ‘‘very encouraging’’, Mr Hipkins said it was ‘‘too soon to speculate’’ on what Cabinet would decide today.
He said testing numbers would be a key piece of information around the Cabinet table today.
Close to 15,000 swabs were taken on Monday, some 10,500 in Auckland alone. That figure was 3379 yesterday.
The results of these tests will be critical when it comes to the advice Dr Bloomfield provides to ministers today.
The Ministry of Health has dramatically increased the number of people considered to be close contacts of the Covid positive family.
On Monday, there were 42 close contacts of the three infected family members, but yesterday Dr Bloomfield revealed that number had more than doubled to 109.
And of the 36 close contacts at Papatoetoe High School, where the daughter goes to school, 22 have yet to return negative tests.
Dr Bloomfield also revealed there were now more than 2000 ‘‘casual-plus’’ contacts the Ministry of Health was following up.
Another key piece of information ministers will consider today is the investigation into how the disease was able to enter the community.
The running theory has been the mother, who worked at LSG Sky Chefs and handled airlines’ laundry, was the first to catch Covid-19 before passing it on to her daughter and husband.
Dr Bloomfield said he was remaining open-minded as to whether it was actually the daughter who contracted Covid-19 first.
Mr Hipkins also revealed yesterday the Government had made major changes to MIQ facilities.
Air filtration systems in all facility lifts were being replaced, CCTV systems had been upgraded and people’s movements had been further limited
- RNZ and NZ Herald