Ministers are set to include plans to limit how much people have to pay towards the cost of care in old age in the government's next spending review.
A spokesman said the prime minister was serious about resolving the issue, after a review suggested there should be a cap on social care of £35,000.
The man who recommended the cap said there was a growing consensus behind the move among political leaders.
However, there has been no agreement on a final package of proposals.
Last month Health Secretary Andrew Lansley said ministers supported the principle of a cap but there was no commitment to finding the money to pay for it.
But the government is keen to scotch the impression that reform of social care in England is dead in the water and a Whitehall source said on Thursday there is a will to include it in the next Comprehensive Spending Review, expected to begin next year.
One option suggested was that it could be funded out of the NHS budget but neither the Treasury nor No 10 were willing to speculate.
Last year the economist Andrew Dilnot was commissioned to examine options for overhauling social care and a £35,000 cap - above which the government would meet the costs - was a key recommendation.
The issue was discussed by the so-called "quad" of senior cabinet ministers last week - including David Cameron and Nick Clegg - and discussions are under way about how the Dilnot Commission's proposals might be implemented.
The Dilnot package would cost the Treasury almost £2bn a year.
A No 10 spokesman said the prime minister and the government were serious about resolving social care but stressed there was no final, signed-off plan ready to be announced.
In a statement, the Department of Health said it was continuing to "explore a range of options" for funding social care in the future.
"As we have said any proposal which includes extra public spending must be considered alongside other priorities at the Spending Review," a spokesman said.
"As we made clear when we published our progress report on care and support funding reform, the government supports the principles of a capped-cost model as recommended by the Dilnot Commission.
"It would, as Andrew Dilnot himself said, enable people to plan and prepare, so that they are not so vulnerable to the arbitrary impact of catastrophic care costs."
'Right way forward'
Mr Dilnot told the BBC he was "delighted" that "significant steps" seemed to have been taken in recent days to agree the basis for a sustainable system for funding long-term care for the elderly.
There was a growing political consensus that a cap of about £35,000 "seemed to be the right way forward", he told Radio 4's World at One programme.
But Conservative MP John Redwood told the same programme that the coalition would "struggle" to pay for such a commitment as previous governments had done.
Many families in the south of England faced care bills of more than £35,000, he said, adding that he would like to see improvements in the quality of care and a system of insurance explored.
The Alzheimer's Society said funding needed to be put in place before 2017 to protect the most vulnerable people - many of whom have been forced to sell their homes to meet care bills.
"If David Cameron decides to follow the Dilnot recommendations, it could end the extortionate costs some people currently pay for care," a spokeswoman for the charity said.
"However, we need meat on the bones of these proposals before we can say for sure what a difference they will make."