Councils in England face a 10% cut in funding from central government as part of the coalition's spending plans for 2015/16, the BBC has been told.
Sources say Communities and Local Government Secretary Eric Pickles has accepted in principle that the £21bn budget could be reduced by this amount.
No final deal has been agreed. The Spending Review is next Wednesday.
Both the Department for Communities and Local Government and the Treasury refused to comment.
In return for accepting such a large cut to local government funding, Mr Pickles is expecting to agree a deal which would see his department take responsibility for other departments' budgets, potentially worth around £3bn.
Councils already get funding from other parts of government to pay for things like road improvements and public health. Under the proposed deal, Mr Pickles would have greater control over budgets like this and make savings in areas where spending currently overlaps between departments.
But it could mean that some health spending would be removed from the so-called ring fence and no longer protected from cuts.
"The wire-cutters are well and truly out," said one minister.
Mr Pickles is also understood to be willing to take more responsibility - and more funding - for the government's work on tackling troubled families. This is currently carried out by a range of different departments such as education and welfare.
On Wednesday Mr Pickles met Health Secretary Jeremy Hunt and Chief secretary to the Treasury Danny Alexander to work through the details.
One source said: "Eric is taking quite a big hit. He has accepted a 10% cut, but he is clawing back £3bn. In terms of spending power (for councils), he can go quite a significant way to make up the 10%. He is also getting some top-slicing from other departments.
"What is happening now is that they (the Treasury) are pressing him to 11%. He is resisting. He is not going to go further than that."
Last month the Local Government Association estimated that a 10% cut in spending would mean an average council having to find another £30m of savings on top of existing cuts.
"In order to achieve that cut, it would have to reduce spending on a broad combination of non-statutory services which might include children's centres, museums and sports centres, as well as reduce road maintenance budgets, increase bus fares and switch off street lights between midnight and dawn," the LGA said.
Whitehall sources made clear that no final agreement had been reached and emphasised that local government spending power would not be reduced by 10% under these proposals because town halls do not just get their funding from central government, but also from business rates and council tax.