While Paul Burstow, the former care minister in the Coalition, said the removal of the benefit for Scots would be "compensated" for by millions of pounds going to Holyrood, the SNP rejected his proposal as part of the UK Government's "sad mantra of dismantling the welfare state".
In a report for the Centre Forum think-tank, Mr Burstow said the £1.5 billion saving for scrapping the Winter Fuel Allowance –worth £200 a year for the over 60s and £300 for the over 80s – would help pay for reforms to the social care system in England.
However, the Prime Minister, who pledged to protect universal benefits at the 2010 General Election, made clear he would not go back on his word.
He said: "I made a very clear promise we would keep the winter fuel payments alongside the other pensioner benefits as they were and that's a promise I'm keeping."
Already, Nick Clegg has raised the issue of restricting universal benefits to the poorest pensioners. Mr Burstow has now floated a plan to use money saved from restricting the Winter Fuel Allowance to cover the growing cost of social care in England; in Scotland care for the elderly is free.
Last year, the Dilnot Commission proposed capping the amount pensioners in England have to pay for care.
Under Mr Burstow's proposal, the Winter Fuel Allowance would be restricted to those on pension credit. At present, those English pensioners with assets over £23,000 have to pay for their care but Mr Burstow wants to raise this level with a cap on contributing to the total cost of care put at £60,000.
Eilidh Whiteford, the SNP's spokeswoman on work and pensions, said: "It is the sad mantra of dismantling the welfare state. Means-testing is a blunt instrument that can create anomalies."
Ros Altman, director general of Saga, added: "Every winter, over 20,000 pensioners die of cold and these excess winter deaths would increase if more pensioners were denied their winter fuel payment."
Andrew Gwynne for Labour said the Coalition was out of touch with the situation.