The income threshold for pension credit, the main benefit to qualify to continue to receive winter fuel payments, is currently £11,800 a year for individuals and £18,023 for pensioner couples.
Designing a new income threshold will now present political and practical headaches for ministers ahead of the Budget in the autumn.
Possible options suggested by commentators and policy experts include linking it to lower council tax bands, or expanding eligibility to those receiving housing or disability benefits.
Resolution Foundation, a think tank, said there were "huge doubts" over creating a new dedicated means test to qualify for the top-up.
It added the most straightforward option would be to expand eligibility for pension credit - but cautioned that expanding this by 10% would cost £2.5bn due to knock-on costs, more than the original policy was meant to save.
Age UK, one of the charities opposing the cuts, welcomed the change in approach but said any new system should ensure pensioners on "low and modest incomes" would be able to keep the payments.
Asked by reporters when the changes would take effect, the prime minister's spokesman declined to guarantee it would be in place this coming winter, but added: "We obviously want to deliver this as quickly as possible.
"We will only make decisions when we can say where the money is coming from, how we're going to pay for it and that it's affordable," he added.