The chancellor is understood to be concerned over the lack of increased spending by the major companies despite them earning huge profits in recent months.
Despite the continued rejection of the notion of a windfall tax by Boris Johnson and senior ministers, the Daily Mail has reported that Mr Sunak is now considering the plan.
The newspaper claimed ministers were left “stunned” when BP chief Bernard Looney recently said his firm’s investment plans would not be affected by such a tax.
He also referred to BP as a “cash machine” despite the growing cost of living crisis hitting households hard in the pocket up and down the country.
Supporters of a windfall tax on companies such as BP argue that it would help families deal with rising costs without an increase in public borrowing.
However, only this week Mr Johnson has continued to resist calls for a windfall tax on energy firms, amid predictions that millions of families could face a further hike of almost £1,000 in bills this autumn.
ScottishPower boss Keith Anderson said average household bills were likely to leap from £1,971 to as much as £2,900 in October when regulator Ofgem next reviews the price cap.
And he said that the government’s current offer of a £200 loan to help households was “not going to be anywhere near enough” to cushion the blow, which follows an average increase of almost £700 in combined electricity and gas prices in April.
Downing Street confirmed that the government is expecting further increases in the autumn, but refused to say whether it accepted Mr Anderson’s figures.
“I think it’s fair to say that we do expect there to be further increases later in the year,” said Mr Johnson’s official spokesperson, adding: “We want to encourage investment and not to deter it and obviously I wouldn’t speculate but obviously we don’t know what impact would be on raising a windfall tax and whether that additional charge will be passed on to bill-payers.”
The shadow energy secretary Ed Miliband said he is in favour of a windfall tax and believes it “could fund real support for families”.
It comes after Mr Johnson vowed on Wednesday to deploy the “maximum energy effort” to help alleviate the crisis, promising more support “in the months ahead”.
In a press conference in Finland, the prime minister said: “We will have the maximum energy effort, ingenuity, to help the British people through them and everybody knows how tough it can be right now.
“But we’re gonna get through just as we got through Covid. And you know all the money we’re already spending, there will be more of course, there will be more support in the months ahead as things continue to be tough with the increase in the energy prices.”