National leader Simon Bridges said it would be outrageous if a bill was passed for the 2020 election and would be seen as "rorting the system."
"It would be entirely wrong."
By the afternoon, Ardern had ruled it out, a move which will disappoint the Green Party which has drawn up a private member's bill that would include lowering the threshold.
Labour and the Greens support four per cent, while New Zealand First supports it staying at five per cent and putting the issue to a referendum. Act also supports a five per cent threshold.
Lowering it to four per cent would reduce the chances of the Greens and New Zealand First being ousted from Parliament altogether at the next election.
The Greens scraped in with 6.3 per cent and New Zealand First won 7.2 per cent of the vote at the 2017 election and small parties often do badly when part of Government.
Bridges said he was open to discussions with the Government on electoral reform.
"We never proactively did anything on electoral law reform without cross-party support.
"I'm available. I'm happy to talk and discuss serious constitutional issues including electoral reform with the Prime Minister."
The last review of MMP by the Electoral Commission in 2012 recommended that the threshold be lowered to four per cent and abolishing the so-called coat-tailing law, ditching the threshold altogether for parties that win an electorate seat.
But there was no cross-party consensus on the recommendations.
An MMP referendum could be added to other questions at the 2020 election – there will be one on the recreational use of cannabis and possible one on David Seymour's euthanasia bill.
Little said it would be preferable to have simple questions with a Yes or No answer.
The Greens have drawn up the Electoral Strengthening Democracy Bill which would overturn the ban on prisoners voting, enable Maori voters to switch rolls at any time, upgrade transparency of election donations and implement the 2012 MMP review.