It was also reported that Mr Johnson will take personal charge of meetings on the energy crisis next week before a decision is taken on any support ahead of 7 February.
In April the price cap, which limits the amount that suppliers can charge, will rise. It is currently at an already record-beating £1,277.
Despite previously floating the option of a blanket removal of VAT from domestic fuels bills during the 2016 Brexit referendum, the measure is unlikely to form part of extra government support, after the prime minister labelled it a “blunt instrument” on Tuesday.
He added such a move would result in a cut in fuels bills “for a lot of people who perhaps don’t need the support in quite the direct way that we need to give it”, but told a No 10 press conference: “I’m not ruling out further measures.”
According to the BBC, extending the winter homes discount, which offers those eligible a one-off £140 payment, to increase the number of people who can claim, is “under discussion with other options”.
Tackled on the issue of rising energy costs for consumers on Wednesday, however, the prime minister’s official spokesperson suggested that there were not any imminent changes planned.
“I’m not aware of any further changes at the moment, but obviously we keep it under review, we are listening to those most affected,” they added.
It comes after concern over a hike in energy bills, which has caused unease in Conservative ranks, was raised at prime minister’s questions on Wednesday, with deputy Labour leader Angela Rayner warning that families were facing a cost-of-living “iceberg”.
Speaking on the BBC Radio 4’s Today programme on Thursday, the Liberal Democrat leader, Sir Ed Davey, also said the government had been “slow to act” to help people who will struggle with rising bills, as he called for a “Robin Hood tax” on oil and gas super-profits.
He also told the Today programme: “The warm home discount, which currently is £140 to two million people, I think we should more than double that to at least £300, but increase the eligibility to seven and a half million people, so many, many more people.
“These are people on universal credit, people on disability benefits, people on pension credit. I want to make sure that working-age families with children get real help with their bills”.
He added: “We’ve got to pay for it. But one of the other effects of the big rising global gas prices, as well as hitting people with their heating bills, is it’s resulted in record profits for the oil and gas sector.
“And I think it’s reasonable to ask firms in the oil and gas sector for a one-off contribution to assist the most vulnerable in society, the less well-off and indeed, actually, energy-intensive industries. I really think the Government has been very slow to act. We’re seeing record profits.”