Number 10 has said scrapping the winter fuel allowance for all but the poorest pensioners is now "not happening".
Earlier on Friday, Sky News revealed the option was under live discussion between No 10, the Treasury and the Department of Work and Pensions as a way to claw back some taxpayer funds from the elderly.
The prime minister is expected to fight the next election on a pledge to keep the pension triple lock despite its spiraling costs, and has been looking at various options to cut back welfare spending as he looks to pave the way for pre-election tax cuts, while also remaining committed to the pensions triple lock at the next election.
One government figure told Sky News that while the option was part of conversations about how to find savings in the welfare bill, No 10 didn't want to risk public speculation on such an "emotive" issue that had divided views across Whitehall.
"Mr Sunak was interested in the option, while the chancellor and work and pensions Secretary Mel Stride were less enthusiastic about means testing pensioner benefits," according to one person familiar with discussions.
One source told Sky News No 10 believes officials in DWP or the Treasury leaked conversations around the winter fuel allowance in order to "kill it off".
Government figures earlier told Sky News the prime minister "understands the politics" of the triple lock and knows he has no option but to recommit to it, given the importance of the pensioner vote to his campaign and the Lib Dem recommitment to the policy in recent days.
Labour is also expected to maintain the triple lock in its manifesto.
"Rishi understands the politics of the triple lock, although he thinks it's far from fair from an intergenerational point of view, so he's trying to redress that a little bit," said one government insider.
Another person familiar with discussions told Sky News earlier that if the government did decide to "keep the triple lock but take away the winter fuel allowance from rich pensioners. I think people will understand that and think it's fair".
Mr Sunak has so far refused to commit to honouring the triple lock - which increases pensions each year by whatever is highest out of average earnings, inflation or 2.5%.
However, insiders say it is inevitable that he will and is now trying to find other ways to offset the cost of the commitment, with the triple lock forecast to cost as much as £45bn a year by 2050.
Winter fuel payments go to about 8.4 million households and is forecast to cost £2bn this year, according to the Institute for Fiscal Studies. A small - and falling - proportion are in receipt of pension credit.
Carl Emmerson, deputy director of the IFS, said over the long-run, the cost of retaining the triple lock will dwarf the saving from even getting rid of the winter fuel allowance entirely, pointing out that since 2010, the triple lock has increased state pension spending by £11bn a year to date.
'Slap in the face for pensioners'
Rachel Reeves, Labour's shadow chancellor, said the Conservatives committed to keeping winter fuel payments and the triple lock in their 2019 manifesto.
"They should not be breaking those commitments", she said. "One thing I would be doing if I was chancellor today would be to have a proper windfall tax on the huge profits that the big energy giants are making and use that money to help people with their bills."
Liberal Democrat Work and Pensions Spokesperson Wendy Chamberlain MP said: "Scrapping the winter fuel allowance would be a slap in the face for pensioners facing soaring energy bills this winter.
"Rishi Sunak must be living on another planet if his thinks this is the answer to the country's problems. Pensioners have worked hard and paid their taxes all their lives, they shouldn't be made to pay the price for the Conservative Party crashing the economy. "
A government spokesperson earlier said the government was committed to the triple lock and said it would not comment on speculation ahead of its annual autumn review of benefits and pensions.
"We have protected pensioners with the biggest State Pension increase in history this year as well as boosting Pension Credit - worth around £3,500 a year for those on the lowest incomes," the spokesperson said.
"On top of Winter Fuel Payments, pensioners will get another £300 this winter to help with essential costs, and we are bearing down on inflation to make everyone's money go further."
But officials also noted that there are 200,000 fewer pensioners in absolute poverty than in 2009/10, with the basic state pension over £3,050 a year higher than in 2010.
Winter fuel allowance is only one spending area the government is looking at ahead of the autumn statement in November.
One figure told Sky News that the Department of Work and Pensions is also considering whether to cut working-age benefits in real terms ahead of the general election as the PM looks for space to create tax cuts. This could mean breaking the link with updating benefits in line with inflation.
PM looking for space to create tax cuts
The prime minister wants to be able to offer tax cuts in the run-up to the election, with one minister suggesting that scrapping the second leg of HS2 as well as a real-term cut in benefits might give the PM more room to do this.
One option being discussed is whether to increase the threshold for paying inheritance tax from £1m to £1.5m in order to appeal to middle-class voters in more affluent counties.
"It might be helpful in some seats," said a figure familiar with discussions, who said scrapping the tax completely carried political risk given it would be framed as a tax break for the very rich.
The issue of the rising tax burden is vexing many Conservative MPs and has been put squarely on the agenda on the eve of the Conservative Party conference after the IFS released analysis showing that Mr Sunak and Boris Johnson have overseen the largest set of tax rises since the Second World War, and will cost the equivalent of £3,500 per household.
The IFS also estimates that by the time of the next general election the tax burden will have risen to 37% of national income and also warns that the shift to higher taxes may never be reversed, piling the pressure on the prime minister to cut taxes as his party gathers in Manchester this weekend for its annual party conference.
Pressure from Tory MPs
Former Prime Minister Liz Truss, who is due to attend the Great British growth rally fringe in Manchester on Monday, alongside former cabinet ministers Priti Patel and Jacob Rees-Mogg, said on Friday: "We should always be seeking to reduce the tax burden, especially when there is so much pressure on family budgets.
"This unprecedentedly high tax burden is one of the reasons that the British economy is stagnating and why we need to cut taxes to help make Britain grow again."
Another senior Conservative MP said some colleagues were in despair over Mr Sunak's leadership and refusal to cut taxes. "We had a majority of 80 and now we'd be lucky to get a majority. We need to demonstrate Conservative values to make sure people can keep more of their money."
Treasury minister Andrew Griffith told Sky News the government still believes in "reducing the tax burden" but their priority is bringing down inflation.
Asked if we can expect some tax cuts before the next general election, he said: "No, that's absolutely not what I'm saying and I think any responsible treasury minister wouldn't come on your programme this morning and make specific commitments."