The Daily Telegraph said the Commons leader told Rishi Sunak at Wednesday’s Cabinet meeting that the increase must be scrapped to stem the rising cost of living crisis engulfing the Government.
The Prime Minister faced questions from all parties – including his own – over the issue in the Commons.
And Mr Rees-Mogg is reported to have said the policy, which was only announced in September to cover an overhaul of social care and to see the NHS through coronavirus, should be ditched.
Earlier, Labour’s deputy leader Angela Rayner told MPs: “The Prime Minister and his Chancellor have presided over economic mismanagement, low growth and neglect of our public services.
“And their resolution to fix this? Whacking more taxes on working people.
“Combine the tax rise with soaring energy prices and the average family faces a hit of £1,200 – this is an iceberg right ahead, so will he finally stop and change course … or will he plough on to what will be a disaster for thousands of families?”
Boris Johnson insisted the Government had taken steps to help people and also “keep this country open, keep our economy moving”.
He said: “We will continue to look after people throughout the pandemic.”
But Ms Rayner countered: “Prices for everyday goods are soaring out of control, hard-earned savings will be hit and the wages of working people won’t go as far.”
Ms Rayner said “serious solutions” were needed to stop people “falling into poverty or debt” as a result of inflation.
The head of the Resolution Foundation think tank said last month that families would face a £1,200 hit by April “from soaring energy bills and tax rises”.
The organisation’s chief executive Torsten Bell said: “So large is this overnight cost-of-living catastrophe that it’s hard to see how the Government avoids stepping in.”
But Downing Street suggested on Wednesday that there are not any imminent plans to help keep energy prices down for customers.
The Prime Minister’s official spokesman said: “I’m not aware of any further changes at the moment, but obviously we keep it under review, we are listening to those most affected.”