The issue is particularly sensitive for Labour's Maori MPs Kelvin Davis, Peeni Henare and Willie Jackson who had spoken in support of the schools in the past and could face a backlash if they are forced to close.
Several are run by Maori or have a high proportion of Maori students and last year Davis said he would resign if the two schools in Whangarei ended up closing altogether.
The three MPs are due to front publicly on the issue today as a group.
Ardern said the three had not raised it with her directly but did support moves to turn the schools into character schools. "And there are cases where schools will fall into that criteria."
She said the point Davis was making was that he believed there was a way forward.
"And so do I. I imagine we are going to find the compromise required."
Hipkins accused National leader Bill English of scaremongering after English described plans to end the schools as "nasty and vindictive" politics driven by ideology and pressure from unions.
"I think Bill English and his colleagues are very much trying to whip up a campaign of fear around the country."
He said Labour had always been clear it would deal with the schools on a case-by-case basis to decide which converted and which closed.
"Ringing round all those schools and saying we are about to close them down is irresponsible because we've got a process in place around how we are going to deal with them."
English has also accused Ardern of being "shameful" for refusing to visit any of the schools to meet students at them.
Hipkins said he would not be at the meeting with the schools because if they applied to be character schools he would have to decide whether to accept it.
That was a legal process which was subject to review, so it would be inappropriate for him to get involved directly in the negotiations.
He denied he had avoided them altogether, saying he visited several prior to the election. He did not believe the schools could not operate under the public school system – and Ardern added the only difference was they would not be able to make a profit.
There are 11 of the schools which have about 1500 students at them. They were developed to cater to students who are struggling in mainstream education.
On Sunday Act leader David Seymour led a march of about 150 supporters, parents and students up Queen St protesting against the moves to end the model.