Downing Street has been in talks with an American millionaire who is interested in helping to set up a pair of twinned academies in east London and Harlem, New York.
Bill Ruane, an investment banker and philanthropist based in New York, wants to build links between education in the US and the UK. He met officials last week.
The meeting comes as the Government tries to court sponsors for its programme to have 200 academies - state schools independent of local councils - open or under construction by 2010.
This week, Tony Blair met the heads of leading private schools, to ask for their backing - and cash - for the project. Several, including Dulwich college, London, have already expressed an interest.
But Martin Stephen, chairman of the influential Headmasters' and Headmistresses' Conference, said that most private schools would not be able to bear the cost.
The head of St Paul's school in London, which charges fees of up to Pounds 17,475 a year, said: "The independent sector generates enough money to run each independent school, by and large.
"It would be very hard for most schools to go down this route. There may be individual schools, but for the majority it is not a viable position."
Academy funding has often proved controversial. Millionaire backers for the programme include Sir Peter Vardy, the car dealer and the fundamentalist Christian, and Philip Green, owner of the Arcadia group.
Mr Ruane, chairman of the $12 billion investment management company Ruane-Cuniff, was introduced to Downing Street by Sir Cyril Taylor, chairman of the Specialist Schools Trust.
Sir Cyril has been involved in importing a range of American initatives to the UK including specialist schools, which were inspired by the American magnet schools.
Mr Ruane was not available to comment, he tries to give his extensive philanthropic work a low profile. But Sir Cyril said that he and Mr Ruane wanted to set up a pair of "special academies" that would work closely and exchange ideas about teaching inner-city pupils. The project would go beyond the traditional twinning that already takes place between hundreds of specialist schools in England and others around the world.
Sir Cyril said that universities would closely examine the work of the academies in Harlem and east London. "There would be a systematic evaluation of what works in the two countries," he said.
It is expected that if the project goes ahead, Mr Ruane would fund the New York school while private companies in the UK would sponsor the London academy.
Mr Ruane already funds places for Harlem children at an independent school in New York and has given support to the Rennaisance accelerated learning programme, an American system for improving English teaching which is being tested in a group of UK specialist schools.
Sir Cyril said the joint academies project could be "a long way off" but that he had been heartened by the first meeting.