Currently, elderly people in England have to contribute to their own care costs if they have savings of more than £23,000.
The Centre Forum report suggests the costs could be met by ending the universal entitlement to winter fuel payment and granting it only to those receiving pension credit.
The report said:
"The Government needs to be clear in its message that a reformed capped funding system is the most appropriate way of dealing with a broken social care system, a crisis that has lasted over 10 years.
"The Treasury needs to grasp the 'best opportunity in a decade' provided by the Dilnot Commission, the goodwill expressed by the financial services industry and by care providers.
"Most importantly it should pay heed to the views of thousands of people who risk losing their entire life's work through having to pay for unexpected and unlimited care costs."
Former care minister, Lib Dem MP Paul Burstow, has called for means-tested winter fuel payments to help pay for elderly care costs
Writing in the Guardian, he said the current system is an "unfair lottery that leaves the exposed to huge care costs".
The majority of pensioners should see their winter fuel allowance cut to help fund a reformed system of care for the elderly, a former minister said.
Liberal Democrat MP Paul Burstow has said only the poorest of pensioners should receive the benefit and savings could help pay for a fairer system of state support for elderly care.
In a report by the Centre Forum think-tank, the former care minister, said the move would help meet the cost of implementing the findings of the Dilnot Commission, which proposed capping the amount individuals have to pay for care during their lifetime.
He suggested setting the cap at £60,000, higher than the £35,000 proposed by the Dilnot Commission, saving the taxpayer up to £1.5 billion a year.