Finance Minister Bill English will release the Budget next month.
Charter or "partnership" schools are different in that they are privately run and publicly funded, and were introduced last year as part of Act's confidence and supply agreement with National.
More schools were opened this year, bringing the total to nine. One of the original schools, Te Kura Hourua ki Whangaruru, in Northland, has struggled and is now under threat of closure.
MartinJenkins, an independent education consultancy, is to carry out the first comprehensive evaluation of the charter school experiment, with its work running until November 2017.
Mr Seymour said some existing charter schools, including Vanguard Military School on Auckland's North Shore, were getting exceptional results, and the process for dealing with Whangaruru had been "very robust".
"You'd have to say if you were going to ask, 'Can we make an assessment of the policy at this very early stage', there is certainly a good case that if we have got quality applicants we should open more schools."
In February, a spokesman for Ms Parata said she "has no plans for another partnership school application round this year". Asked yesterday if that was still the case, he said the minister had nothing further to add on the subject.