An American-based firm has expressed interest in setting up a charter school in New Zealand.
But opponents of the schools say overseas organisations should not be publicly funded to run schools - potentially for profit - in New Zealand.
The Government is working towards more charter or "partnership" schools beyond the five which started this year.
Applications for the next round, to open next year, close next Tuesday and officials will not say who is interested until then.
But the NZEI and PPTA education unions say Ministry of Education staff have confirmed an unnamed United States-based company has expressed interest.
Overall there have been 18 formal "indications of interest", including from those who missed out last time.
Applications need to be made to the Partnership Schools Working Group, a panel headed by former Act Party president Catherine Isaac.
She told the Herald she could not name organisations that had expressed interest.
"I can confirm that an overseas organisation has made an inquiry, but whether that will translate into an application I honestly don't know.
"We had quite a few overseas organisations last time making inquiries."
The US has more than 5600 public charter schools in 42 out of 50 states, and one in 20 students nationally attends a charter school, according to Moody's Investors Service.
NZEI national secretary Paul Goulter said the union was "absolutely alarmed" at the prospect of a US-based firm starting a charter school here.
"The American education system is clearly in disarray ... I don't think New Zealanders want private companies beating the path towards New Zealand's education system."
Education Minister Hekia Parata said she had not been told of any intention by an international business or group to apply to establish a school.
She said priority would be given to new partnership schools that cater for primary-age students, are based in areas of roll growth and can show they are in areas where students are not served by the education system.
Also favoured will be those who "offer innovative options for 0- to 8-year-olds".
Alwyn Poole of the Villa Education Trust, which runs the South Auckland Middle School, said high-quality proposals from overseas should be considered.