The controversial annual limit on total household income from a range of benefits was introduced on Monday at the level of the average salary of £26,000, amid claims that it will force many families into hardship.
But The Times reported that Conservative MPs want it cut further to £20,000 as part of an assault on welfare spending if Tories win the 2015 general election.
The move would open up a political dividing line with Liberal Democrat coalition partners, who have acted as a brake on Tory ambitions to slash back the welfare state.
An aide confirmed that Mr Osborne had received representations on lowering the cap, adding: "We want to see how the policy beds in. But clearly over time, lowering the cap is an option."
Work and Pensions Secretary Iain Duncan Smith has already floated the idea of limiting child benefit to two children for jobless households and stopping housing benefit for under-25s who could live with their parents.
Braintree MP Brooks Newmark, a Tory member of the Commons Treasury Committee, told The Times: "I think many people would be in favour of bringing it down to the real average post-tax pay. I can't see Essex Man complaining if that happened."
Mr Duncan Smith said a "very, very significant number" of people had found work in affected households within the four London boroughs where the cap has already been implemented. "The key principle behind this all over the country is that those who work, those who are trying to do the best in their households, do not see others who are down the road, who are on benefits, on welfare, actually getting more than they do," he said.
Conservative party chairman Grant Shapps insisted further radical reforms were being considered, including capping child-related benefits for unemployed parents with two children. Child benefit, income support or tax credits could be withheld for the extra children under the plan, Mr Shapps told the Daily Mail. In another proposal, under-25s who are unemployed should be denied housing benefit so they continue to live with their parents for longer, the minister said.