Chancellor Kwasi Kwarteng is expected to make a statement in the next hour, reversing the proposed scrapping of the 45p rate of income tax, 10 days after it was announced in the mini-budget.
The U-turn comes after several Tory MPs voiced their opposition to the plan.
Government sources are yet to comment on the reports, which would mark a humiliating climbdown for Liz Truss.
Ex-cabinet minister Grant Shapps had warned the Prime Minister would lose a Commons vote on the proposal.
The plan to scrap the 45p rate, paid by people earning over £150,000 a year, had been criticised as unfair at time of rising living costs.
On Sunday, the prime minister told the BBC she was absolutely committed to it as part of a package to make the tax system “simpler” and boost growth”.
But the measure has seen remarkable opposition from the markets, opposition parties and a growing number of Tory MPs.
Increasingly, it seemed Ms Truss did not have the numbers to get it through.
On Sunday, senior Tory Michael Gove hinted he would not vote for the plan when it came to Parliament, saying “I don’t believe it’s right”.
The former Cabinet minister said the PM’s decision was “a display of the wrong values”.
Mr Shapps also urged Ms Truss to U-turn, warning her not to have a “tin ear” to voters’ concerns about rising living costs.
“I don’t think the House is in a place where it’s likely to support that,” he told the BBC on Sunday.
The U-turn, suggestions of which were first reported by the Sun, comes on the second day of the Conservative conference in Birmingham, with Mr Kwarteng due to speak later on Monday.
The pound jumped on the news, rising by more than a cent against the dollar to $1.1263.
The currency touched a record low last week after Mr Kwarteng’s mini-budget – which contained around £45bn of unfunded tax cuts – created turmoil on the markets.