Government subsidies are scheduled to be scaled back from next month, meaning average annual bills would rise to 3,000 pounds ($3,594.00) from 2,500 pounds now, Reuters reported.
But the Times said the lower bills would now be kept in place until the end of June.
Hunt is due to deliver a budget statement on March 15, when any extension to the level of support could be announced.
Opposition parties and campaigners have urged the government to change course and keep providing its current level of help to households, many of which are struggling to meet the rising cost of living even before bills rise.
Hunt can count on a roughly 30 billion-pound windfall as he prepares his budget, according to the Institute for Fiscal Studies (IFS).
Keeping the current level of energy subsidies would cost 2.7 billion pounds until the end of June, based on current energy price forecasts, the IFS estimated this week.
Under the government’s energy price guarantee mechanism, which was set up last September, taxpayer money has been used to shield households from the surge in prices that followed Russia’s invasion of Ukraine.
Wholesale prices are expected to fall over the three months from April to June meaning the government’s guarantee will no longer be necessary beyond after that period, The Times citing a Whitehall source.
The Finance Ministry did not immediately respond when contacted by Reuters.
Energy companies are already preparing to amend bills to reflect the current level of support being renewed rather than reduced in April, according to a separate report by the BBC on Friday.