Prime Minister Tony Blair believes the academies, which are directly funded by Government and independent of local councils, are the key to improving education in England.
A dozen academies have opened since 2002 and a further 41 are due by 2007 but schools report problems finding the sponsorship they need to gain the status.
A Number 10 source said officials were looking at ways schools could become academies without constructing new buildings. They must currently raise at least pound;2m from private sponsors to cover 10 per cent of the building costs and then receive the rest, often around pound;18m, from the Government.
The "ultimate aim" would be to let all secondary schools bid to become academies, he said, although the status might be given a different title.
Schools can only apply to be academies now if they are based in disadvantaged areas.
Richard Bird, head of Casterton community college in Lincolnshire, said many heads might be tempted by academy status because they seemed to offer even greater independence than grant-maintained schools. "Academies are like grant-maintained schools on steroids," he said.
However, the Department for Education and Skills said that academies were different from the GM schools because they worked more collaboratively with local authorities and had a member of the LEA on their governing body.
It is unclear what the involvement of sponsors would be in the new-style academies.
Mr Blair has applauded moves by private schools to become academy sponsors.
Other sponsors have included finance companies, religious groups and the chairman of the Saga group, which specialises in holidays for the over-50s.
Reading FC this week became the third football club to announce it would be sponsoring an academy following Bristol City and West Bromwich Albion The Secondary Heads Association said the fact the Government was thinking about dropping the pound;2m sponsorship requirement showed the academies had failed to attract sufficient interest from businesses.
John Dunford, general secretary, of the Secondary Heads Association, said: "The Conservatives' city technology colleges failed because insufficient sponsors could be found. It appears to be the same case with academies.
"There is no real evidence that there is any benefit from the diversity between schools which the Government is trying to promote."
When Mr Blair spoke at the Capital city academy in Brent earlier this year he said he hoped many more academies than planned would be open by 2007.
"Academies are a prime example of the innovation we seek," he said.
"They have a wholly new, independent governance structure which comes from the relationship with an external sponsor who brings not only a financial endowment but also vision, commitment, and a record of success from outside the state school system."