This would be the first time a financial cap has been imposed on individual council services - limits imposed by previous governments applied to the total spending of each authority.
Downing Street has told the Department for Education and Employment that it must curb central spending by councils from next April.
Civil servants have four areas in mind - school improvement, special needs, transport and strategic management - and are considering three options. These are an overall cap for the four; a cap exempting special needs; or individual limits for each service area. They are not expected to affect school budgets directly, but could have a knock-on effect.
The move, which is a major shift in policy, was revealed at a highly-charged meeting between civil servants, council officials and leaders of the grant-maintained sector.
It comes less than two months after the Government announced that councils would have to delegate an extra Pounds 1 billion, starting from April to cover areas such as repairs and maintenance, inspection and school meals.
DFEE officials have already warned of the dangers of limiting "the different and very sensitive" spending on special needs.
In a paper presented to a working group looking at council funding they said: "We should be wary of capping it without much greater investigation and consideration."
And this week the Local Government Association called for an urgent meeting with David Blunkett, the Education Secretary, vowing that the proposals would be fiercely resisted.
It predicted less parental choice amid warnings of cuts in transport and claimed that capping would damage the standards drive.
Sir Jeremy Beecham, LGA chairman, said: "Crude capping will hinder progress. That is not just expenditure on administration but on frontline support services such as special needs, education welfare and school transport. "
He claimed capping ran counter to Labour's election manifesto and said that it would mark a U-turn by Mr Blunkett who in 1985, as leader of Sheffield, opposed Tory plans to cap council spending.
Graham Lane, LGA education chair, said: "We are bitterly opposed to these plans. They are a lunacy. They are an attack on children with special needs and they will lead to admissions problems."
But the move has been welcomed by the grant-maintained - soon to be foundation - sector.
Pauline Latham, chairman of the Grant-Maintained Schools Advisory Committee, said: "It is a victory for common sense."