Ministers at Westminster do not currently allow private firms to profit from running their own state-funded schools, although they can earn management fees by providing services to schools run by other groups.
Internationella Engelska Skolan (IES) in effect aims to end this distinction, while remaining within the law, by linking up with parents and other non-profit groups prepared to hand over control of their free schools and carry the IES brand.
The company, which runs a chain of around 17 free schools in Sweden, says it is in talks with eight potential secondary or all-age free school operators in England.
The move will be watched with interest from across the border in Scotland, where the Scottish Conservatives say they want to introduce new independent schools outside council control.
A mixture of educational charities, not-for-profit trusts and private firms could run the schools. The independent schools would be state-funded but management would be devolved, giving them control over how they were run and their curriculum, say the Tories.
Last year, Education Secretary Michael Russell returned from a fact- finding trip to Sweden, enthusiastic about what he had seen in some of the free schools he had visited there. But since his visit, he has done little to support any moves to go down that road in Scotland.
In England, IES's potential partners include groups of parents, groups of teachers and an unnamed local authority which it says is "seriously interested".
But for the partnerships to go ahead, IES says other parties will have to be happy to hand over a large amount of decision-making to the company.
The National Union of Teachers claimed the plans proved that the coalition Government's free schools policy was about "privatisation".