If the currently developing depression did, it would be named Cyclone Freda, the second named cyclone this season, following Cyclone Evan.
The forecast came as Samoa declared a water crisis and Fiji dealt with a typhoid outbreak as a result of Evan.
The new weather system was 2700km nor-northeast of Auckland, which was the area that nurtured cyclones that have in the past reached New Zealand.
The Regional Tropical Cyclone Centre in Nadi, Fiji, this morning said global models were giving the system a moderate to high chance of becoming a cyclone and moving south-southwest.
The US military's Joint Typhoon Warning Center in Hawaii rated it in its last bulletin as a low chance of being a cyclone.
The centre earlier this month constantly rated as low the chances of another depression becoming cyclonic - and it became the deadly Evan.
Fiji's independent forecaster NaDraki Weather said the system would move close to New Caledonia around New Year's Eve and shouldn't directly affect Fiji.
The Samoa Prime Minister's Department this morning said the death toll from Evan remained at five with 11 people still missing, nine of them at sea and two in the area of Apia battered by the flooding Vaisigano Basin.
"Water supply for the entire country is critical and a forecast for when reliable supply will be available nationwide is yet to be determined," the department said.
It said the cyclone had destroyed much of the hydro power system that supplied Apia and Upolu. Generators were submerged in mud and debris.
Two big diesel generators suffered severe water damage and power production had been cut back by 60 per cent.
Meanwhile in Fiji, where one person was killed in Evan, the military regime had restricted all movement around the village of Koroboya, near Ba, due to an outbreak of typhoid, a water born disease that can be fatal.
In October, New Zealand's National Institute for Water and Atmosphere said they were predicting "near average or slightly above average numbers of tropical cyclones for the 2012-13 season.
On average there are10 named tropical cyclones in the southwest Pacific each season.
They said tropical cyclone activity east of the International Dateline was expected to be normal, with above normal activity for Niue and Tonga during the second half of the season.