The Education Minister says the Government is open to the idea of tertiary institutions setting up schools under the partnership school scheme.
There are five of the publicly-funded private schools, which are modelled on an overseas system known as charter schools, in which the state contracts organisations to run schools.
Minister Hekia Parata said tertiary institutions have expressed interest in running such schools.
The Government will analyse the performance of the first partnership schools next year, she said.
"We are certainly very open to the idea because of course we want to make sure that we are meeting the needs of every child."