Ministers are expected to announce the measure on Thursday in a bid to plug the funding gap in care services for the elderly and disabled.
Under the plans, local authorities will be able to accelerate council tax increases already pencilled in for this parliament by the former chancellor George Osborne.
Mr Osborne announced in November 2015 that councils would be able to raise council tax by 2% a year between 2016/17 to 2019/2020 to raise almost £2bn in social care. But under the new proposals, councils are expected to be allowed to front-load those planned increases to bring in more money sooner.
Senior government sources told Sky that councils will be allowed to add 3% to council tax bills next year and a further 3% the year after as long as the money is spent on social care.
This could see the average council tax bill rise by nearly £100 over the next two years: a 3% increase to the average Band D property bill of £1,530 (2016/17) amounts to £45.80 a year.
Under Mr Osborne's original plan the average council tax bill would have gone up by 2% a year over three years to 2019/20 - an average of about £30 a year.
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