Mr Sunak has been urged by climate activists and opposition MPs to go further on his windfall tax as oil and gas giants' profits soar.
He and Chancellor Jeremy Hunt are seeking ways to plug a multibillion-pound fiscal black hole.
Mr Sunak is considering expanding the windfall tax by increasing the levy or including renewable energy generators, The Telegraph reported.
Downing Street said “nothing is off the table” before Mr Hunt’s autumn budget on November 17.
Shell has avoided paying the levy despite a doubling of profits fuelled by soaring energy prices.
Mr Sunak and Mr Hunt are also exploring tax rises and public spending cuts worth up to £50 billion ($57.84bn) a year to fill a hole in public finances, the Financial Times reported on Thursday.
Rishi Sunak through the years - in pictures
Ministers are hoping the measures will not have to be implemented in full as part of the fiscal statement on November 17, the FT said.
But officials want the government to use the £50bn estimate after being given weak economic forecasts by the Office for Budget Responsibility.
The £50bn figure comes from Treasury calculations showing an initial fiscal hole of between £30bn and £40bn.
That will require tax rises or spending cuts of about £45bn because attempts to fill it will worsen the economic outlook, which will in turn hit future tax revenues, the newspaper reported.
Can Rishi Sunak tame the UK economy? - Business Extra podcast
New polling indicates that the elevation of Mr Sunak to Conservative leader might have registered with approval among some voters.
New polling by YouGov put the Tories on 23 per cent to Labour at 51 per cent, a four percentage point bounce for the Conservatives from a week ago.