"Very few" of the 1,280 schools belonging to the body that represents the independent sector would take up a Tory offer to join the state system, its chairwoman has said.
Dame Judith Mayhew Jonas, chair of the Independent Schools Council, said that only smaller, struggling schools would be likely to consider the option - as a way of avoiding closure, merger or takeover.
Speaking before the ISC's annual conference in London next Tuesday, she said: "I don't see a huge number of ISC schools wanting to give up their independence, governance and financial management. It is the essential DNA of the sector.
"Our schools do value their independence and the freedom they get in relation to the curriculum, the ability to include more art, music and sport and they value the fact they are not over-regulated.
She said she would be surprised if financially viable schools with good headteachers and strong governance would want to trade in some of their freedoms for state funds. Existing parent-run schools, both within and outside of the ISC, might consider the option, she said, but it was uncertain how they would react to the offer.
"The more struggling schools, the proprietor schools that have no obvious succession, who face merging with another school, might consider changing their status. These are the schools who I anticipate will be considering this very carefully."
While welcoming the idea of increased choice and diversity in schools, she also expressed concerns about exactly how "free" the new schools would be.
She pointed out that private schools already have the right to apply to become state-funded academies, but only a handful had done.
At the last count, six private schools have become academies, including Belvedere Academy in Liverpool and the Bristol Cathedral Choir Academy.
Meanwhile, Michael Gove, the shadow education secretary, sketched out his hope to draw private schools into the state system in a speech last week.
Addressing the annual conference of the Association of School and College Leaders (ASCL), he said he would "explicitly love to see more children educated within the state system".
The invitation to bring private schools into the state sector would form part of Tory plans to create a network of so-called "free schools", free to vary the national curriculum and set teachers' pay, he said.
Under the controversial plans, they hope groups of parents or teachers, voluntary organisations and private business will set up their own state-funded schools.
The policy was criticised last week by John Dunford, general secretary of the ASCL, who warned that it could create a "cornershop" education system, made up of many small, competing schools.
"We do not want a return to the bad old days of dog-eat-dog policies in the false belief a good dose of the market will improve standards," he said.
The Tory plans are likely to be a key topic for debate at the ISC's conference, where Dame Judith will launch the council's manifesto for the next government. Its "wish list" is likely to include a call to cut back on red-tape in the independent sector.
Academies that were once private schools
Belvedere Academy, Liverpool
Birkenhead High School Academy, Wirral
Bristol Cathedral Choir Academy
Colston's Girls' School, Bristol
The Hereford Steiner Academy, Herefordshire
William Hulme's Grammar School, Manchester.