The consultants would provide "specialist technical advice" and outside scrutiny.
But the Corrections Association, which represents prison officers, said the consultants were "hired guns" who offered little value.
"They quickly work out what the payer wants them to say and they research to that," said the union's president, Beven Hanlon.
Ms Stevenson refused to say how much a public prison would have cost to set up, or put a figure on the prison's total construction cost. Internal Corrections documents suggest it could be about $300 million.
PPP schemes overseas have been criticised for employing large numbers of lawyers, accountants and consultants.
The Haringey local council in London spent £24 million ($46 million) on consultants before it started its school-building programme.
Conservative MP Richard Bacon told the Financial Times this year: "It is clear that [PPP] has spawned an entire industry of advisers who have done extremely well out of it."
Corrections' business case says the costs of a PPP "will be higher" than those of a public prison, because private companies pay more to borrow money and need to make "commercial returns".
The deal will be cheaper only if the company can run the prison 10 to 15 per cent cheaper than the department.
The Corrections Association said a private firm would "most definitely" make savings by cutting staff and wages, putting prison safety at risk.
Three consortiums, all headed by Australian security firms, have been shortlisted for the contract, expected to be signed by July.
The numbers
* $11 million sum the Government will spend on consultants for the new men's prison at Wiri
* $10 million sum spent on internal costs before the prison is built
* 18 companies employed by Department of Corrections on the project
* 960 number of beds proposed new prison will have
