Private schools have offered to create 10,000 free places for poorer students but only if the Government helps fund them.
The move comes after Prime Minister Theresa May warned in a Green Paper that private schools would have to do more for society if they want to keep the tax privileges that come with their charitable status.
The proposal, by the Independent Schools Council (ISC), suggests the Government pays no more than the cost of a state school place per pupil - thought to be around £5,500 a year - with the private sector paying the rest. The places would be available to students of all ages, from prep school to sixth form.
Some children would be tested for ability, but the ISC said it is not aiming the places at top academy or grammar school pupils, but families on lower incomes.
ISC chairman Barnaby Lenon said: "The proposals we are putting forward go considerably further than some of the ideas the Green Paper suggested and, by helping create more good school places, both in state and independent schools, we would be helping to expand real social mobility in this country."
But outgoing Chief Inspector of Schools Sir Michael Wilshaw said the plan does not go far enough.
"I think they can do better than that and if I was Government I would be asking them to do more as a quid pro quo for their tax privileges."
Labour former education secretary Baroness Estelle Morris, an ex-teacher, told the BBC Radio 4 Today programme: "This is about a request to use state money, taxpayers' money, to extract the brightest children out of our comprehensive schools and skim then off and put them into public schools, and that's not good for the education system."
Critics have long questioned the charitable status of private schools because most pupils come from wealthy families.
Mike Buchanan, chairman of the Headmasters' and Headmistresses' Conference, an association of chiefs of leading independent schools, said: "This innovative plan could herald a new era of co-operation between Government and independent schools to offer outstanding education to a new generation of children from lower income homes.
"Offering jointly-funded places in independent schools is a high-impact, low-risk idea which will be zero additional cost to the taxpayer.
"Those schools already give free and partly-funded places to thousands of children to try and offer them the best possible start. We want to do more, and hope the Government will put pupils before politics and work with us to offer them this life-changing opportunity."
T he ISC proposal was announced on the same day a report by the Sutton Trust revealed that children judged to be from "just about managing" families were "significantly" less likely to attend a grammar school than their wealthier counterparts.
The report said that, even when children are similarly bright, the most economically disadvantaged are still under-represented in selective schools.
A Department for Education spokesman said: "Our proposals are about creating more choice, with more good school places for more parents in more parts of the country.
"We want to do this by lifting the ban on new grammars, and harnessing the resources and expertise of universities, faith schools and independent schools.
"We welcome contributions to the consultation and will respond in due course."