Changes to child benefit are "hugely popular" with most voters, a Treasury source has told the BBC.
The government will remove the benefit from households in which someone earns more than £42,475 in January 2013.
The source said only 15% of taxpayers would be hit, and polling suggested 77% of voters backed the move.
Downing Street has rejected Labour's call for the "really unfair" plan to be dropped, but says changes may be made to how the new policy is implemented.
Deputy Prime Minister Nick Clegg had earlier told the BBC that the government would "look at how you administer the removal of child benefit from upper-rate earners".
Mr Clegg acknowledged it was an anomaly that a family with a single earner taking home more than £42,475 would lose child benefit but a couple each earning slightly less than the top rate could together take home £80,000 and keep the benefit.
He said: "What you do when you create these cut-offs is you create some sort of anomalies... there's a specific issue about how you administer the removal of child benefit from upper-rate earners and we've always said we will look at exactly the way that that is administered."
The Daily Telegraphreports the cut-off point might be raised to £50,000, but Mr Clegg said no final decision had been made.
He suggested details would be announced in the Budget on 21 March - adding that his priority was a rise in the threshold at which people started paying tax.
A Treasury source described the latest claims of a government rethink over child benefit as "speculation".
He said: "We have not said how we will implement it (child benefit) but will do in due course."
In January, Mr Cameron gave the first hint of a government rethink when he warned of the "cliff edge" some families might face with the removal of child benefit for all top-rate taxpayers.
Labour raised the planned child benefit cut during a Commons debate.
Shadow chief secretary to the Treasury Rachel Reeves accused ministers of showing a "lack of competence and care" by introducing "crude" changes.
She said: "We urge the government to review and rectify the pressure they are piling on to families, already under huge strain."
Treasury minister David Gauke replied that the child benefit cut for higher earners would redirect money to those "who need it the most".
He said: "I fully understand that child benefit is a vital income boost to parental income for millions of families across the country.
"But at the same time it comes as a substantial cost to the Exchequer, making up around of 7% of total social security and tax credit spending each year, including payments of over £2bn a year in child benefit to higher rate taxpayers."
Labour says it wants to keep child benefit for all, but adds that it cannot pledge to reinstate it in the future because it would depend on the state of the economy at the time the party came into government.
The Treasury has previously said the child benefit changes would save £2.4bn in 2013-14 and £2.5bn in 2014-15.