Justice Minister Andrew Little doesn't think political parties should be state-funded, saying it's "not our culture".
The Greens say it's an idea worth considering, to "remove the influence of powerful vested interests".
"Our democracy is precious and needs to be protected," co-leader Marama Davidson said last week, in the wake of claims the National Party had been splitting donations to avoid breaching declaration thresholds.
"It is time to consider major donation reform so that there is more transparency, and powerful vested interests no longer have influence within political parties."
Under the law, donations to parties under $15,000 can be made anonymously. Former National MP Jami-Lee Ross accused leader Simon Bridges of ordering a $100,000 donation to be broken up into smaller pieces so the donor's identity could be kept secret.
Mr Little said some changes are possible before the 2020 election, but increased state funding is probably not going to happen.
"We need to make sure we have an election donations regime that avoids at least the inference being drawn that there is unhealthy influence being wielded," he told Newshub Nation on Saturday.
He said it's "not our tradition, it's not our culture" for taxpayers to foot the bill for parties' campaigning.
"I think it's a healthy thing for parties to have to go out and do their fundraising and earn their keep. There is some state funding of political parties - we see that with the broadcasting allocation each election. This is all ground for fertile debate, and maybe it is timely for us to have it."
Four out of every five dollars donated to political parties is done so anonymously. National received $3.5 million in anonymous donations in 2017.
The Greens want the threshold dropped to $1000.
"This means that small donations at local fundraisers aren't mired with red tape, but also means politicians will find it much harder to hide donations from powerful vested interests," says Ms Davidson.
The Taxpayers' Union slammed suggestions of state-funding, saying "taxpayers shouldn't be forced to promote ideas that they disagree with or even find morally reprehensible".