All schools could be funded directly from Whitehall under a radical plan which the Prime Minister is understood to be considering.
The Government is again under increasing pressure to sort out education finance following the annual battles over departmental spending and the teachers' pay award.
Ministers and local government leaders have long argued over who is responsible for school funding levels. Councils regularly claim that annual Government grant settlements are responsible for cuts, while ministers argue that council inefficiency is to blame.
The issue has intensified this year with the widespread protests by parents and governors and heavy lobbying of MPs.
Any move to centralise school funding is unlikely before the next general election, but ministers close to John Major are pressing for a commitment to be included in the party manifesto.
Downing Street would not comment on a report in The Times this week that the Government was planning to take responsibility for school funding away from local councils.
Past Conservative governments have considered but rejected such a move, which would involve one of the biggest upheavals for local authorities in recent history and deprive them of their largest responsibility.
According to The Times, the issue is back on the agenda again. It previously surfaced when local councils lost their control of polytechnics and colleges in 1993.
The Department for Education and Employment and the Funding Agency for Schools - the body which oversees grant-maintained school finance - are already working on a national funding formula for schools.
This would be a key component in the move to centralise school funding, but is an area fraught with difficulties.
Gillian Shephard, the Education and Employment Secretary, has already acknowledged that it would produce winners and losers and with the general election looming it may not be politically expedient to make more enemies.
Sir Malcolm Thornton, chairman of the House of Commons select committee on education, claimed this week that centralising funding would be disastrous for primary schools.
He said statistics showed that Pounds 500 million would theoretically be transferred to primary schools if they all left council control.
Subtracting the cost of a funding agency for schools, estimated at Pounds 100m, and dividing the remaining Pounds 400m between 21,000 primary schools, produced a figure of about Pounds 15-Pounds 20,000 extra for each school, out of which they would have to provide all the central services currently supplied by the local education authority.
"This amount is only enough to buy one extra teacher, never mind all the advisory and other services needed," he said. "There may be a case as far as secondary schools are concerned, but these figures blow the gaffe on talk of all this wonderful freedom that will be available for primary schools.
"I don't want my party to go down a road which I believe is fundamentally wrong. Whatever I can do to try and stop them making that mistake I will. "
Sir Malcolm told delegates at a one-day conference on education organised by the Council for Educational Advance he strongly opposed proposals to abolish education authorities on political as well as financial grounds, because they provided important checks and balances.
Local authority associations said the plan to take school funding away from them amounted to a nationalisation of the education system.
Baroness Josie Farrington, chair of the Association of County Councils, said: "This is a bizarre suggestion given it comes from a Government which claims to be in favour of parental choice."