Local councils face a 10 per cent cut in funding from central government as part of the coalition's spending plans for 2015/16, according to a BBC report.
The BBC says Local Government Secretary Eric Pickles has accepted that the £21bn budget could be reduced by this amount in next week's spending review.
In return, Mr Pickles may take charge of road and public health budgets - which also contribute to council funding - and be able to make savings in areas where there are overlaps.
It could mean that some health spending would no longer be protected from cuts, the BBC says.
On Wednesday Mr Pickles met Health Secretary Jeremy Hunt and Chief secretary to the Treasury Danny Alexander to work through the details.
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.
Bournemouth council leader John Beesley was among those who signed a letter to the government last week calling for an end to cuts.
But the BBC says Whitehall sources say 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.