Iwi were successfully running large businesses in many sectors, and there was no reason why they could not manage prisons, Foon said.
"If you can trust Serco ... to come run our prisons with great failure, why don't we try iwi?
"They have great capability, capacity, and Māori have said what is good for iwi is actually good for New Zealand."
Foon said the success of the Rangatahi Courts in lowering recidivism rates, and kura kaupapa and wānanga in boosting academic achievement, showed the benefit of Māori-led programmes.
He said iwi should not just be running prisons and that the Māori economy should work with the Government on housing - as people released from prison face difficulties securing accommodation.
"And also ensuring that there are jobs. And iwi are right into the world of business: horticulture, agriculture, forestry, fishing, building developments.
"The whole supply chain downstream from prison, to learning a trade or some skill at least that is transferable on the outside and having real work out there, I think that will reduce recidivism a lot.
"And if it trends like that, how I predict it to, I'm sure ... you could actually have Māori running the rest of the prisons in New Zealand because of that model."
Ngahiwi Tomoana, the leader of Ngāti Kahungunu, told Morning Report he hadn't heard from Foon about the concept but admitted it was something his iwi had considered anyway.
"We'd run it with the intent of closing it down over the next few years because it's a travesty that our people are 50 per cent of the male population and 68 per cent of the female population," he said.
He said the iwi had the capacity, skills and institutional knowledge to run them, but "we also have the capacity and institutional knowledge to restore and rehabilitate everybody so eventually we can close them down."
He said there was a clear link between people losing their jobs and numbers entering the prison system in Hawke's Bay.
If iwi did run the prisons, it would be done in partnership with whānau, and they would use their connections with the corporate world to find employment for inmates upon release, he said.
The theoretical side of a job would be covered in prison, while basic literary and numeracy skills would also be improved.
He called on the minister to meet with iwi to discuss the plans.
"We've talked about this for a couple of decades now in my time, and our elders, when the prison was being built, they asked that half the amount of money being spent on the prison be used in kura kaupapa and we'd keep people out of prison."
Corrections Minister Kelvin Davis declined an interview but said in a statement he had not been approached by Foon about the idea.
Davis said the Government did not support establishing private prisons, regardless of the operator.
He said Corrections had introduced a new Māori co-designed strategy to decrease the Māori prison population, and increased money for other Māori programmes.
Davis said progress has been made in safely reducing the prison population, which had recently dropped below 9000 for the first time since 2015.
