David Cameron wants his old school – Eton College – to set up and run an academy funded by the taxpayer.
The Prime Minister confirmed that he met representatives from the £31,000-a-year boarding school this week to discuss taking over a state secondary.
Eton joined several other leading private schools at a Downing Street reception on Thursday staged to drive forward the Coalition’s flagship education reforms.
It is the latest in a series of attempts being made by the Government to court the independent sector as part of an expansion of the academies programme.
Earlier this summer, Nick Gibb, the Schools Minister, also addressed a meeting of the Headmasters’ and Headmistresses’ Conference, which represents 250 leading fee-paying schools, over the issue.
The move is likely to infuriate teaching unions who are already opposed to academies which they see as the effective “privatisation” of state education.
But talking to the BBC, Mr Cameron insisted that the sponsorship of academies represented a “great way” for independent schools to fulfil their “charitable purpose”.
Asked if he wanted his former school to formally join the programme, he said: “Yes, I would like all private schools to engage in this agenda and if you look at most private schools many of them already run bursaries for children from less well - off backgrounds and partnering state schools.
“To me all private schools have always had a charitable foundation, a charitable purpose, and that's a great way to deliver that.”
He added: "The truth is the problem has been not enough good school places in our country...so anyone who can play a role in that - private schools included - is welcome through my door to talk about how we drive up standards."
Tony Little, the Eton headmaster, said that the Eton had close relations with local state schools and was examining "several possible routes" for greater involvement and "ruled nothing out".
An expansion of academies is being seen as central to the Government’s attempts to drive up standards of state education.
Under reforms, schools are given almost complete freedom to run their own policies on admissions, the curriculum, teachers’ pay and the shape of the academic year.
Top state schools are automatically given the right to apply for academy status.
Ministers also want the worst schools to make the switch under the leadership of a third party sponsor – usually outstanding state schools, charities, education companies and entrepreneurs.
Some 28 independent schools are also helping to run academies, including Sevenoaks, Dulwich, Wellington, Marlborough, Malvern, Winchester, Uppingham and Oundle.
But ministers are keen to get more independent schools involved.
Mr Cameron joined Eton at 13 and left in 1984. Lord Waldegrave, the former Conservative Cabinet Minister is currently the provost of Eton and attended Thursday’s meeting.