Thirteen per cent of voters wanted Labour to cut the Greens out and govern with just NZ First, while 22 per cent favoured Labour governing with the Green Party only.
Only four per cent of respondents chose the status quo of both NZ First and the Greens as part of a Labour Government.
The poll of 1000 people aged over 18 was taken from August 12 to 16, and has a margin of error of +/- 3.1 per cent.
Nine per cent of respondents selected 'other' and 17 per cent were not sure. A National Party option was not included in the poll question.
Labour has governed in a coalition with NZ First since 2017 with the Green Party providing confidence and supply.
Prime Minister Jacinda Ardern has refused to say what her own preferences would be or whether she would include any other parties if Labour could govern alone.
However, Green Party co-leader James Shaw has made it clear he wants a Labour-Green Government without NZ First.
The current governing arrangement has also sometimes frustrated Labour's supporters who considered NZ First was a barrier to reforms Ardern had wanted.
While support for a Labour–NZ First government was low, NZ First leader Winston Peters could take some heart from the 13 per cent who did prefer it over Labour alone or the Greens.
It indicated Peters' message that it could be a 'handbrake' on Labour's policies was having at least some traction among voters wary of a second Labour Government.
NZ First is polling well below the five per cent needed to get back into Parliament, and is aiming to persuade National Party voters to cast a strategic vote to stymie a Labour or Labour–Greens Government.
The National Party has ruled out partnering with NZ First.
Dr Lara Greaves, an Auckland University politics lecturer, said it was likely some National voters picked the NZ First option in the poll because of the handbrake argument.
However, whether that translated into actual votes for NZ First remained to be seen.
"There is potential those voters will be convinced especially now Winston has that extra month to try to convince people to vote for NZ First."
There has also been speculation that if National voters decided it had no chance of winning, they could vote for Labour to ensure it was not left relying on the Green Party. Greaves said that would be minimal.
"I don't think that many people who are National voters would turn to vote for Labour. Just the physical disgust or discomfort of being a National voter and having to vote for Labour strategically is quite difficult for National voters," Greaves said.
On recent polling, Labour is well placed to get a majority itself. If it does so, it will be the first party to do so since MMP was introduced in 1996.
Support for Labour governing alone was higher among older New Zealanders aged 60 plus (46 per cent) who have experienced First Past the Post governments.
Support for a Labour-Green government was more popular among younger voters. Thirty per cent of those aged 18-29 wanted it.
