Chancellor George Osborne is considering lowering the maximum amount families can claim in benefits to £20,000 a year, Treasury sources say.
A £26,000 cap on the total amount of benefits that people aged 16 to 64 can receive, is coming into force in England, Scotland and Wales.
Critics say the changes will not tackle underlying problems of worklessness.
But Treasury sources say the cap could be lowered in future if it is shown to work.
An aide to the chancellor confirmed reports in the Times newspaper, saying George Osborne wanted to see how effective the cap was at reducing the benefit bill and getting people back into work.
The aide told the BBC: "We've had representations. we want to see how the policy beds in, but clearly over time lowering the cap is an option."
Mr Osborne has faced pressure from some of his own MPs to signal a further move on the cap, in the run up to the next general election in 2015.
Under the new system, couples and lone parents will now not receive more than £500 a week, while a £350 limit applies to single people.
The cap, not yet law in Northern Ireland, is said to reflect the average working household income.
It has already been implemented in four London boroughs - Haringey, Enfield, Croydon and Bromley - since April.
The benefits cap applies to people receiving jobseeker's allowance, child benefit, child tax credits, housing benefits and other key support from the government.
The Department for Work and Pensions estimates about 40,000 households will be affected.
There is no cap on people who receive disability living allowance or its successor, the personal independence payment, as well some other benefits, such as industrial injuries benefit or a war widow or widower's pension.
Those in receipt of working tax credits are not affected by the cap, but it will apply to those who get £59.75 a week carer's allowance, to help them look after someone with "substantial needs", and people in receipt of Employment and Support Allowance.
About £95bn a year is currently paid out in benefits to families of working age.
The government hopes the cap will save about £110m in the first year, and £300m over the next two years.
Critics say the cap fails to tackle underlying issues, such as the difficulty of finding work, the cost of housing and regional differences.
In a separate development, Conservative party chairman Grant Shapps said child-related benefits for unemployed parents should be capped at two children.
Child benefit, income support or tax credits could be withheld from families who have a third child under the plan, Mr Shapps told the Daily Mail.
The minister also suggested unemployed people aged under 25 should be denied housing benefit so they continued to live with their parents for longer.
"Welfare should not be a way of life," Mr Shapps told the Mail.
"If you are a working family and you have another child, you know it's going to mean quite a severe impact on your living costs. Yet in the welfare system, it's almost turned on its head, so additional children are actually recognised, with no limit."
Addressing the housing benefit proposal, he added: "A young person who's out of work is given an advantage over a young person who's in work when it comes to moving away from their parents because of housing benefit.
"So there's a bizarre incentive which means if you're not in work you can more easily move out and get your own place. That is a matter of basic fairness."