The government will allow local authorities in England to increase council tax by 2% to cover a funding shortfall in adult social care, George Osborne is expected to announce.
The Local Government Association says there will be a shortfall of more than £2.9bn in care services by 2020.
The association is urging the government to address "this crisis" in its Spending Review.
The chancellor is set to reveal more in his Autumn Statement on Wednesday.
BBC economics reporter Rob Young said there were concerns from those who worked in social care about how to ensure the money raised was not used for other purposes.
Others have questioned whether the measure would raise the sums needed, our correspondent added.
Health think tank the Kings Fund says adult social care has had its budget cut by 9% in real terms since 2010.
It says the cut in spending has happened at a time when demographic pressures mean that the cost of providing care for older and disabled people is increasing by 3% a year.
In August, the chief inspector of adult social care in England, Andrea Sutcliffe, warned cuts were putting care under "stress and strain".
She said funding cuts had led to carers feeling overworked and under-valued, undermining the work they do.