Greens Party co-leader James Shaw says the relationship with Christopher Luxon is "good" but "fundamental" issues with the National still apply.
It comes after the latest TVNZ Kantar poll saw a dramatic swing with National pulling ahead of Labour for the first time since the start of 2020.
National was on 39 percent support, up 7 percentage points, ahead of Labour which was on 37 percent, down 3 points.
The Green Party is holding steady at 9 percent, ACT is down 3 points to 8 percent while both the Māori Party and New Zealand First are on 2 percent.
Shaw told AM on Thursday he hopes Luxon continues his work on climate change but the relationship between the two parties was in a holding pattern.
"Every time these numbers shift around, we get asked if we would entertain the possibility of going into government with National," he told AM.
"The relationship with Christopher Luxon is good, he did a lot of work when he was in the private sector on climate change so we hope that work continues because they have been very wobbly on that recently.
"The main issue with National from our perspective is, other than changing the leader the rest of the party hasn't changed.
Shaw told AM that even though National is under the new leadership of Luxon, the ideology of the party still remains the same "which ultimately distribute wealth from the lowest income in the country to those on the highest incomes in the country".
The Greens have worked with National in the past.
In 2008, they signed a Memorandum of Understanding when National took office, where the two parties worked together on a home insulation scheme, energy efficiency and the regulation of natural health products.
The relationship continued after the 2011 election but was eventually ended by then Prime Minister Sir John Key who said while they had done some good work together it had become clear the Greens just did not want to be with National.
*Article changed to reflect Shaw wasn't specifically asked whether Greens would work with National.