The Association of Metropolitan Authorities is to recommend that its 68 members switch the start of the financial year from April to September to enable schools to plan more easily.
The Funding Agency for Schools, which administers and monitors spending in the GM sector, is also considering the change following requests from heads.
Work is at a very early stage but Cecil Knight, chairman of the Grant-Maintained Schools Standing Advisory Committee, said: "It is really about matching resources more accurately to needs."
Mr Knight, head of Small Heath School, Birmingham, said many opted-out schools had to wait seven months before they were paid for extra pupils who started in September. "Some LEAs don't fund the increased number of children until the following April and in popular, rapidly expanding GM schools quite a lot of money is involved," he explained.
Conversely, opted-out schools with falling rolls in September often receive "a bonus" because the money is not taken away from them until the following April.
If developed, the proposal for change in the GM sector is likely to operate initially only in the 22 local education authorities which are using the common funding formula.
The Association of Metropolitan Authorities will recommend the move to its members this autumn.
Schools currently get their budgets in April but have to plan from September to August - in effect across two financial years.
But while education officers are keen to see the change, it may be difficult to get town hall treasurers to agree as it would involve underwriting a third of school budgets because they would fall in the traditional April-March financial year.
The financial year for further education colleges and universities already matches the academic year.
The proposal for the GM sector is in the FAS three-year plan, which also reveals the quango's intention to develop a "map" of schools in which there is a strong case for change of character. Another priority is to ensure that GM schools play a full part in nursery education expansion.