Recent polls suggest National and ACT could form a government together, but National might also have to rely on NZ First - who ACT has ruled out.
National has also begun ruling out - or in some cases merely rejecting - ACT policies.
Seymour said if National was not prepared to "fully share power", his party would consider a minority-government position.
This type of governing arrangement would require the larger party to seek the minor party's backing for all government spending, on a case-by-case basis, including the Budget.
"If they don't agree with us about the magnitude of change that is required for New Zealand to turn itself around, so we're basically [saying]: 'OK Chris, we promised we'd support a change of government, so you'll be the prime minister but we're going to sit down at the end of every Parliament and you'll need to come and talk to us about every single vote'," Seymour said.
"That will be gruelling and challenging, no question."
National leader Christopher Luxon on Monday dismissed the possibility as hypothetical and speculative, saying he did not think it would become a reality.
"What I'm saying to you is that David Seymour and I have a good relationship. We have known each other for a long time, we were neighbours for four years, our personal relationship is good.
"We will be working constructively through the issues and policies. I think we'll have a very constructive working relationship and I've got every confidence in that, as you've seen in previous National-ACT governments as well."
'A form of brinkmanship'
Otago University law professor Andrew Geddis told RNZ the confidence-only proposal would certainly be an innovation in the MMP era, and while likely a negotiating ploy - it must be taken seriously.
If National and ACT had the majority in the House and both said they would give confidence to Luxon to become prime minister then the Governor-General would appoint him.
Fairly soon after the election, the new government would have to put together its spending plans to bring to Parliament to be authorised.
In essence, ACT seemed to be saying if they did not think enough of their policies were part of the new government's agenda, National could start a government - but they would have to keep talking to ACT about policy and keep consulting on an arrangement to run the country.
However, Prof Geddis said Seymour had outlined "slightly different things".
"At one point, it seems to be 'every time you want to spend money you must come to us and get us to agree to that spending'.
"At other points, he said, 'no, no, what we'll set up is essentially an overall cap, an overall envelope of spending and tax that National would have to work out how to fit within'."
If it was the latter, it was essentially "a veto", which was different to the way these arrangements had worked out under MMP in the past.
The Greens, for instance, from 2017-2020 voted for government Budgets even though they were doing it under protest.
ACT was saying it would not vote for any Budget it did not like and as a consequence the government would collapse and a new election would be needed.
"So it's a form of brinkmanship: it's saying 'meet our demands or we will bring the government down'," Prof Geddis said.
