A grassroots petition for a National/Green coalition - not authorised by either party - has gathered more than 3700 signatures.
Christchurch organic fashion entrepreneur Clive Antony, a National supporter, said he started the petition to initiate a "conversation" about a possible coalition of the two parties.
"It started to annoy me that everyone has been ruling out a National-Green coalition and rightly so as both parties have basically written it off," he wrote on the website change.org.
"But they have left the smallest of doors open. That's where we come in!
"I genuinely think there is common ground between the National Party and the Green Party, which could result in practical policy wins for New Zealand. Environmental issues such as carbon neutrality and social issues like child poverty come to mind."