The schools would have their auditors appointed instead by the Audit Commission, which supervises local authority spending.
A joint Treasury and Cabinet Office inquiry team is looking at audit arrangements for appointed bodies that receive public money - including GM schools, further education colleges and Training and Enterprise Councils. It has been warned that the philosophy of "public audit" demands that auditors should be chosen not by the schools but by an outside supervisory body.
The same rule would also be applied to such bodies as housing associations which are also currently free to select their auditors.
Another proposal before the team is that responsibility for auditing should be separated from grants and policy. This would mean big changes at the Funding Agency for Schools, which supervises both.
The team is taking these proposals seriously since they have been made by the Audit Commission, which also supervises spending by the police and probation service, and much health service work.
The audit review team, led by a Treasury official, Kingsley Jones, is due to produce a consultation paper next month.
It was set up after the first report of the Nolan Committee on standards of conduct in public life, which raised questions about inconsistencies in the way local public bodies are audited.
GM schools usually appoint their auditors from local firms of accountants, but they also have to file financial reports with the FAS. The GM Schools Foundation says arrangements work smoothly. The FAS in turn has its books monitored by the National Audit Office, which reports to the House of Commons Public Accounts Committee. The NAO also regularly investigates a sample of GM schools to check for financial irregularities.
But local authorities complain that nobody is properly responsible for value-for-money studies of GM schools while their own schools are studied in detail by the Commission. Ian Langtry, of the Association of County Councils, said: "We expect the same audit arrangements to apply to schools of all kinds."
The FAS says it recently re-issued its "rainbow pack" giving details on how and what schools should report on. A spokesman said its own value-for-money unit will shortly publish a study of maternity cover in GM schools.
One problem being studied by the TreasuryCabinet Office review afflicts further education in particular. It is "auditing overload".
Martin Evans, of the Chartered Institute of Public Finance and Accountancy, said some further education colleges were in theory subject to 14 sets of auditors. "Audit and accountability are huge subjects. Ideally we should have a royal commission which would start with a blank sheet of paper."
Bill Ogley, of the Audit Commission, said: "We do need to create reporting lines so there is no more than one auditor coming through the door." He denied the Commission is "touting for business", but the Cabinet Office review is considering handing all local public bodies, elected and non elected, over to it.