New Prime Minister Liz Truss used her victory speech to pledge to "deliver on the energy crisis" by dealing with bills as well as supplies.
A freeze on energy bills is understood to be one of a number of options being worked on to help struggling households to cope with soaring costs.
It is expected that energy suppliers will be able to take out government-backed loans to subsidise bills.
Energy bosses have been meeting with government officials on the matter.
A £100bn plan to freeze household bills was proposed by energy companies last month.
Under the proposal, bills would be subsidised and the current price cap of £1,971 for a typical family would be maintained for two years.
The BBC understands that a similar scheme will be used to limit the energy price increases being experienced by small and medium-sized businesses.
And bigger companies may be offered tax breaks to help them through the period of high prices.
'Bold action'
Ms Truss beat rival Rishi Sunak with 57% of party member votes to become the new Conservative leader.
Speaking after the announcement, she said: "I will deliver on the energy crisis, dealing with people's energy bills but also dealing with the long-term issues we have on energy supply."
In response, Labour leader Sir Keir Starmer said: "There can be no justification for not freezing energy prices.
"There's a political consensus that needs to happen. She needs to ask the question, how she's going to pay for that? Labour made it clear, it needs to be a windfall tax on oil and gas companies."
Ms Truss's team is understood to have been working on a support package for energy bills "for weeks". An announcement on what they will do is pencilled in for this Thursday.
"Lots of measures have been considered, some have progressed and some have not," a source told the BBC.
Business groups welcomed Ms Truss's appointment but urged her to take "big bold action" to help firms who, unlike households, are not protected by an energy price cap.
Federation of Small Businesses chairman Martin McTague said soaring energy bills "must be addressed urgently."
And Tony Danker, the director general of the Confederation of British Industry, said he was "hopeful" that businesses would receive help.
"The cliff edge that's coming on new energy contracts [for businesses] are astronomical, and need smoothing," he told the BBC.
"I'm pretty hopeful this week that not only will the new prime minister tackle energy bills for households, she'll also look at businesses too."
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