Broadcaster and author Toby Young is in talks with two Swedish for-profit organisations to run his proposed school in west London.
Mr Young, author of How to Lose Friends and Alienate People, has been holding discussions with both the International English School and Kunskapsskolan to take over the day-to-day running of his school.
If successful, it would be only the second time that a secondary school has been run by a profit-making company. Turin Grove School in Edmonton, north London, was taken over by US firm, Edison.
The Government is opposed to mainstream state schools being run by for-profit companies. The Conservatives have also said they are, but they are open to the idea of private companies being brought in on "full-service" contracts.
Mr Young said the parents and teachers of the school would act as sponsors, but either of the two Swedish providers would operate the school.
"The main reason we want to bring in a provider is to address the issue of continuation that can occur with parent-founded schools - what do you do once the first cohort has gone through the school?" he said.
"They both have very good track records as education providers. An alternative would be to enter into a relationship with an existing academy sponsor, but they are less willing to get involved unless they become the main sponsor."
Mr Young added: "There is something quite attractive about bringing someone in to operate the school on a full service contract."
The practice is backed by shadow schools secretary Michael Gove, but the idea has been greeted with scepticism by the teaching unions.
Mary Bousted, general secretary of the Association of Teachers and Lecturers, said bringing in private providers will be "fraught with unintended consequences".
"This is yet another ill thought-through, headline-grabbing idea," Dr Bousted said. "Running schools is a serious business and has to be approached seriously, and my worry is this hasn't been approached seriously at all.
"Toby Young seems to want to move away from a monolithic local authority education provider to a monolithic private education provider. We saw in the US what effects privately run schools can have and it led to lots of schools having to be closed down, this seems equally fraught with unintended consequences."
The NUT said that Tory support for Mr Young's proposal belied the Conservatives' pledge to introduce parent-led schools, adding that it "totally opposes" the plans should they be realised.
NUT general secretary Christine Blower said: "Those who run and manage schools should be education professionals with a public service ethos, not educational companies whose bottom line is serving the interests of their shareholders. Children and young people are not commodities; they are entitled within school to know that those who run and manage their school have purely their educational interests at heart.
Ms Blower added: "Toby Young's suggestion of bringing in private companies on a service contract gives a lie to the Conservative's stated intention to introduce parent-led free schools. In practice, parents do not have the time or the expertise to run their own schools.
"The Conservative's plans can lead in one direction only and that is the introduction of profit-making companies into the running of the English education system."
See Swedish free schools, pages 32-34
Four kids in need of 'tough love' and Latin
Toby Young first declared his intention to open his own Swedish-style free school last year in order to give his four children the best start in life, while keeping them in state education.
His proposals were for a "comprehensive grammar school", which would teach a narrow curriculum and espouse subjects such as Latin and "tough love" discipline.
His disclosure that he is in talks with both International English School and Kunskapsskolan may come as a surprise considering the differing approaches of the two, but Mr Young believes both have an impressive track record for delivering a "fully academic" curriculum.