Private schools will offer to provide up to 10,000 free places a year to low-income families in England.
The Independent Schools Council (ISC) says if the government pays £5,550 per place - the cost in the state system - the schools will cover the rest. This is expected to cost up to £80m. Some pupils would be tested for academic ability but the scheme would not just target the brightest children.
The proposal, originally seen by the BBC and now confirmed, will be made in the ISC's response to a government consultation on the future of education.
The scheme would be open to primary and secondary school-age children. But details about which families would benefit and what form the tests would take are yet to be settled and the scheme could not take place without the government's approval.
Currently it costs an average of £30,000 to send a pupil to board and £15,500 for a day school for a year.
The plan is designed to meet government demands that - in exchange for its tax-free, charitable status, which saves independent schools at least £150m a year - the private education sector does more for potential pupils whose families cannot afford to pay the fees.
There are roughly 600,000 pupils in each year group in England, and private schools educate only 7% of the total school population.
The ISC said its offer would provide a number of school places equivalent to building 10 state secondary schools. It says it already provides 40,000 bursaries worth £350m, but only 5,500 of these provide fully funded places.
