The Tory leadership favourite will invite applications for drilling licences in new fields and as many as 130 will be issued, according to insiders quoted in The Times.
First Minister Nicola Sturgeon has previously rejected calls to maximise oil and gas drilling in the North Sea, arguing Scotland should instead accelerate its transition to renewable and low-carbon energy.
Last year, she said the Cambo oil field off Shetland should not get the green light.
She told MSPs: "I don't think we can go on extracting oil and gas forever, and I don't think we can continue to give the go ahead to new oil fields.
"I have set out a proposal for a climate assessment and I think the presumption would be that Cambo could not and should not pass any rigorous climate assessment."
UK business secretary Kwasi Kwarteng and Jacob Rees-Mogg, the Brexit opportunities minister, have reportedly been meeting with oil and gas companies in a bid to secure energy supplies this winter. This includes maximising domestic production.
Mr Kwarteng is expected to be made Chancellor if Ms Truss wins the leadership race.
The controversial Rosebank field off Shetland is among the projects set to be supported by Ms Truss, The Times said.
Labour Party chairwoman Anneliese Dodds warned the “massive increase” in the cap on energy bills “will plunge many, many households into financial distress”.
Asked about reports Ms Truss would support oil and gas drilling licences in the North Sea and if that was the answer, Ms Dodds told Times Radio: “No, it’s not and the answer really is to be taking action to get the cost of those bills down.
“Labour’s been very consistent on this. We’ve got a fully-costed plan that would enable the Government to not be going ahead with that massive increase in the cap on energy bills that’s projected to be coming through very, very soon, that will cause – well it’s causing households worry right now, but that will plunge many, many households into financial distress.”