Bolger said most New Zealanders shared the Green Party's goals of a cleaner, greener New Zealand and National could be persuaded to move closer to its position on climate change and cleaning up rivers.
Until now, the people urging Greens to consider talks with National have come from outside the party.
That includes senior National ministers who have floated the idea of a National-Green coalition in a bid to strengthen their hand in talks with NZ First leader Winston Peters.
But a former Green MP, Nandor Tanczos, has joined the crowd saying that a coalition with National should be an option - but only in future elections.
He said it would be "political suicide" to go with National this year because it would be a betrayal of Green voters who were told this would not occur. It was also practically impossible because of the party's requirement for any coalition deal to be backed in a vote by 75 per cent of members.
But unless the party opened the door to National in future elections it would "continue to play out the dynamic of this election over and over", Tanczos said.
"We may be mighty in opposition, but we will always be puny in coalition until we stop relying on discontented Labour voters for support."
Green Party leader James Shaw has not ruled out talking to National about forming a Government, but has said that his party campaigned on changing the Government and many of National's policies were "incongruous" to Green values.
Green MPs last week said the party would not stomach a coalition with a party which had spent the past nine years expanding oil exploration, increasing the agricultural footprint and building more roads.
There are some areas where National and Greens broadly have common goals, in particular on water quality, protecting biodiversity, and reducing greenhouse gas emissions.
It is the pace and method for achieving these goals where they differ - something which National insiders say could be changed in any National-Green talks.
National Party pollster David Farrar predicted that by going into Government with National the Greens could secure $1 billion for cycleways, a levy on nitrate pollution, a higher emissions reductions target, and a doubling of funding for the Department of Conservation, along with other major concessions.
Common Ground: National and Greens
1 Biodiversity/pest control - National have set a goal of ridding NZ of pests by 2050, and could be open to the Greens' policy of doubling funding for Department of the Conservation rangers.
2 Climate change - The two parties fundamentally disagree on whether farmers should be accountable for their emissions. But National could be persuaded to lift its emissions target.
3 Water quality - National could be persuaded to act faster on cleaning up New Zealand's rivers, or increase the number of rivers which will be cleaned up.
4 Public transport - National is increasingly under pressure to fix Auckland's transport woes, and could agree to Green policies like bringing forward rail from the CBD to the airport.
