NZ First leader Winston Peters said the NZ First caucus would discuss the bill before making a decision.
However, he said entrenching the seats would not necessarily offer more protection since the entrenchment itself could easily be overturned by a simple majority of Parliament.
"If you think you think you can entrench the Maori seats, the law to remove the entrenchment legislation does not require 75 per cent. It only requires a bit more than 50 per cent. And there you have it. It doesn't work and I think that's the defect in the idea."
The Electoral Act's section 268 requires a 75 per cent majority or referendum to repeal or amend the electoral system, the term of Parliament, the general seats, and the voting age.
However, section 268 itself can be amended by a simple majority – so the Maori seats could be taken out of it again easily in the future.
National has previously opposed entrenching the seats and has a longstanding policy to abolish those seats which was put on ice during its governing arrangement with the Maori Party.
Leader Simon Bridges said the matter would have to be decided by the caucus.
During the election campaign Prime Minister Jacinda Ardern said she supported entrenching the Maori seats and hoped to ensure that happened.
The issue was left to be dealt with by a member's bill rather than a government bill presumably because of NZ First's objections.
Tirikatene said he was "quietly confident" he could secure the support to pass the bill.
He said it was a disparity in electoral law that the general seats had a higher level of protection than the Maori seats and he believed both should be treated the same.
He was yet to discuss the issue with NZ First.
NZ First is in coalition with Labour but between them National and NZ First have enough votes to get a majority and it has already sided with National against Labour three times on member's bills.
This week NZ First supported National MP Harete Hipango's bill to exempt the bosses of voluntary organisations from liability for new health and safety requirements – something Labour opposes. It will now be considered by a select committee.
National and NZ First also defeated a Labour MP's bill to allow MPs to take the Parliamentary oath in a language other than English or te reo Maori.
Earlier this year it also sided with National to support Simeon Brown's Psychoactive Substances Amendment Bill to select committee. That was opposed by Labour and would increase the maximum penalty for supplying psychoactive drugs from two to eight years' jail.
Mitchell said there was more license for NZ First to vote according to its own policies and views on member's bills because they were not government bills.
"Private member's bills are an opportunity to show some independence by each of the parties. It's not a government bill so you can have a difference of opinion."
We've always been a party that takes the personal politics out of it and goes on supporting a policy rather than the people or party that is putting it forward."
He said NZ First would give Labour a heads up under the no surprises policy when it intended to vote against it.
