Scottish Power has already put forward a plan costing £100 billion ($115bn) for a two-year energy bill freeze that will be financed by loans underwritten by the Treasury.
The proposal is backed by other energy companies, the report says.
One energy company source said Truss campaign members have “extremely actively explored” the idea, with Kwasi Kwarteng, the Business Secretary tipped to become chancellor if Ms Truss wins, appearing “very open” to options for a freeze.
Another industry source confirmed the proposal was being scrutinised by Ms Truss's campaign.
“I’m confident there will be a mechanism introduced that freezes bills," the source said.
Another said the idea had been discussed “quite a lot in the last fortnight", a Truss insider said.
The specifics of such an energy bills freeze – who would benefit, for how long, at what price and the degree to which the taxpayer would cover the cost – remain points of debate, sources say.
A Truss campaign spokesman declined to comment.
The foreign secretary, widely tipped to defeat rival Rishi Sunak when the Tory leadership winner is announced on Monday, said she will be capable of making “difficult decisions” as prime minister to get the UK through the energy crisis.
The UK's energy crisis explained - video
There have been ever-louder calls in recent weeks for the government to intervene to support the most vulnerable, with energy bills set to rise to around £3,500 this winter for the average household.
But on Sunday, Ms Truss repeatedly declined to spell out her plans to tackle soaring energy bills.
“I will act immediately on bills and on energy supply because I think those two things go hand in hand,” she said.
“We need to deal with the immediate problem, we need to help people. We need to help businesses. But we also need to sort out the supply issues.”
Repeatedly pressed for details, she said: “Before you have been elected as prime minister, you don't have all the wherewithal to get the things done.”
Writing in the Sunday Telegraph, she promised to appoint a council of economic advisers to help guide her and her chancellor.
“I understand how challenging the cost of living crisis is for everyone. These are tough times and the months ahead will be hard,” she wrote.
Ms Truss said that she would take “immediate action” to tackle the cost-of-living crisis for families and businesses, while also delivering a “broader plan to get our economy growing, make it more resilient and make it more competitive”.
“If elected, I plan within the first week of my new administration to set out our immediate action on energy bills and energy supply.
“A fiscal event would follow later this month from my chancellor, with a broader package of action on the economy.
“We need to take the difficult decisions to ensure we are not in this position every autumn and winter.
“Sticking plasters and kicking the can down the road will not do. I am ready to take the tough decisions to rebuild our economy.”
Everything you need to know about Liz Truss - video
Mr Sunak also refused to give details of his plans on energy prices except to say he would help people who are struggling with paying their bills.
“It wouldn't be right or responsible for me to sit here and give you the exact to the pennies and the pound, and that's because I'm not inside. I haven't seen all the numbers and nation's finances,” he said.
Everything you need to know about Rishi Sunak - video
Recent days have been full of speculation about who could make up the Cabinet in a Truss administration.
There is also a growing expectation that the next prime minister will make an early visit to Kyiv to shore up support for Ukraine.