The ministry owns the buildings but had no responsibility for their design, construction, finance or ongoing maintenance.
It is understood the consortium behind the Hobsonville school, Learning Infrastructure Partners, would earn $100,000 over its 25-year contract.
The new super school proposed for Christchurch would see Aranui High School, Wainoni Primary, Aranui Primary and Avondale Primary closed from December 2016.
Ms Parata announced this in an interim decision on May 22. The schools have until July 3 to give feedback on the plans, and a final decision will be made in September.
The proposed school would be built on the Aranui High School campus.
The minister also disagreed with closing Chisnallwood Intermediate and with further consultation on the idea of setting up two schools on the Aranui High School campus - a year 1-6 school and a year 7-13 school on the one site.
Principal of Aranui High School John Rohs supported a year 1-13 school, but said a public-private partnership would detract from the community approach the school was trying to achieve.
"We are opposed to this. The needs of our community are not conducive to the public-private partnership."
Mr Rohs said it had come as surprise to see the minister had put forward the PPP procurement option.
Chairwoman of the Wainoni Primary School board of trustees Christine Nihdam said the school supported a year 1-13 school, but had only recently heard about the public-private partnership proposal.
"We haven't had a chance to discuss that matter yet. It was something that had not been mentioned previously. It's was something new to us."
The Ministry of Education's deputy secretary for regional operations Katrina Casey said a business case for a public-private partnership would be developed later this year.
She said the business case would analyse the PPP cost against the ministry's standard procurement model.
"The Ministry is required to assess the requirement for PPP for all capital projects using Treasury guidelines. At this stage the ministry is not aware of any specific interest from the private sector to build the campus."
The ministry already uses the private sector to build schools, but a PPP extends the responsibility to include design, build, finance and maintenance of the school over a long-term contract of up to 25 years.
"One of the main benefits for a school is that that the board of trustees and school leadership no longer have to worry about maintaining school property as this is the responsibility of the private partner," Ms Casey said.
"This means the Board can focus on teaching and learning and improving educational outcomes."
A spokeswoman for the ministry said none of the reports from the ministry had discussed procurement methods.
"A business case will be developed later this year to determine whether a PPP for Aranui and other Christchurch schools provides better value for money than a more traditional contracting method.
"No decisions have been made to fund Aranui year 1-13 school using the PPP model at this stage but as the Minister has indicated she would like a PPP to be considered."