Between 1986 and 2013 Māori home ownership dropped 20 per cent, while the proportion renting went from 41 to 77 per cent.
The Māori home ownership rate was 43 per cent compared to 63 per cent for the general population, and Māori were five times more likely to be homeless than Pākehā.
"Māori are more likely not to own a home and be stuck in the rental trap, at the same time many are either on minimum wage or just above and not keeping pace with the cost of living," Tukaki said.
Māori also struggled to develop collectively-owned land.
"No bank is going to give you a mortgage to put a house on Māori land because of the risk profile," Tukaki said.
"They are worried if you default they won't be able to get their hands on the land under the mortgage."
The Māori economy, including iwi-owned businesses, has been estimated to be worth over $50b.
Māori businessman and Ngāti Whātua Ōrakei director Renata Blair said a Māori bank was a "logical step".
"A lot of iwi are already almost acting as banks, financing loans, some have saving schemes, so I think a bank is a natural progression.
"I think people would also like to see banks owned by iwi that kept profits in New Zealand, and reinvested it back into social, cultural, environmental and business areas."
He Korowai Trust CEO Ricky Houghton raised the idea of a Māori bank back in 2002, and was still a strong supporter.
His organisation was helping relocate people to their ancestral lands and building emergency housing for whānau in the Far North. Houghton said he regularly ran into problems accessing finance for their projects.
"These Australian-owned banks are treating Māori as second-class citizens.
"A Māori bank would be the best thing that could ever happen for Māori.
"In the Far North we have 75,000 hectares of undeveloped, underutilised Māori land. We might be cash-strapped but we are resource rich."
EY social sector leader Hamiora Bowkett said while a Māori bank could be a solution, it might not be the "silver bullet".
"You can't lose sight of the fundamentals. If you have got a good proposal, good track record and are able to generate income to cover costs of capital, you are going to get finance from a bank.
"There can be a problem with our people not being able to organise themselves to work with commercial providers so they can manage risk."
Other finance options included iwi and the Government acting as brokers, underwriting financing or providing cheaper mortgages, and even a Māori infrastructure fund.
A similar institution had been set up over a decade ago in Canada, called the First Nations Finance Authority.
The FNFA provided "investment options and capital planning advice and, perhaps most importantly, access to long-term loans with preferable interest rates".
It had facilitated hundreds of millions of dollars in loans to dozens of First Nations, which has funded infrastructure, social and economic development, land purchases, independent power projects, and community housing.
TDB corporate finance and economics advisers director Phil Barry said while he could see the appeal in setting up a Māori bank, he was not sure it would address the underlying causes of low Māori home ownership rates.
"Is the problem access to finance? Or is the root problem low income levels, levels of educational qualifications and skills, and things like collective ownership of land that are making it hard for some to access finance?
"Where Māori have sufficient income and the ability to repay a loan, is there any shortage of people willing to lend them money?"
Barry said he was concerned a Māori bank could end up with an "adverse selection" problem.
This was where the bank could end up attracting and serving the high-cost, high-risk clients no other bank wanted.
"These people may be the ones who need finance but will the bank itself be able to survive without considerable support from its shareholders in what is a competitive environment?"
