The plan is part of a government drive to reduce living costs, amid rising prices for fuel and food.
Boris Johnson has told his ministers he wants to reduce childcare costs by easing health and safety rules, the BBC has learned.
Sources say the PM wants to lower the legal limits on adult supervision in England, as part of a drive to reduce living costs.
Ministers are under pressure to act on the cost of living, as rising inflation pushes up the price of food and energy.
Mr Johnson is said to be frustrated action has not been taken already.
The issue has been raised a number of times at cabinet in recent weeks, and the Department for Education has been looking at how to relax the rules.
Opposition parties have said government help with living costs is insufficient, with Labour and the SNP calling for an emergency Budget on more support for households.
Current legal requirements in England stipulate there must be at least one member of staff for every three children in groups aged two years and under.
For two-year-olds and over, there must be one member of staff for every four children.
Sources say Mr Johnson told his ministers to get on with lowering these limits at a cabinet meeting on Tuesday to address the cost of living.
No 10 has said the PM wants ministers to explore “innovative ways” to ease living costs – with proposals sent to the government’s domestic and economic strategy committee for further discussion.
Downing Street said this committee would meet “in the coming weeks to finalise the proposals”.
At the meeting, Chancellor Sunak drew attention to financial assistance already on offer, including including £9bn targeted towards helping people with energy bills.
A council tax rebate worth £150 and a cut to fuel duty were both announced by Mr Sunak earlier this year.
The prime minister’s official spokesman said the chancellor “underlined the importance” of not fuelling further inflation, and that departmental budgets “are set” with no plans to currently go beyond these limits.
The Liberal Democrats said the prime minister’s cabinet meeting showed he was “completely out of ideas during the most profound crisis in decades”.
“Whilst families are facing sky rocketing bills and soaring inflation, Boris Johnson’s answer is another quiz night at Number 10,” Lib Dem leader Sir Ed Davey said.
He called for an emergency budget that would cut VAT and introduce a “windfall tax on the super profits of the oil and gas companies”.
Labour has made a similar proposal, saying its own “emergency budget” would include a cut to energy bills funded by a windfall tax on oil and gas companies.
‘Booming profits’
It comes as Labour has warned of a £10bn hike in annual petrol and diesel costs, with “soaring” prices putting the squeeze on household budgets.
“Labour’s plan would help households through this crisis with up to £600 cut off energy bills, funded by a one-off windfall tax on the booming profits of oil and gas producers,” said Labour’s shadow secretary of state for transport, Louise Haigh.
The SNP called for an emergency budget earlier this month, saying the Tories had ignored the cost-of-living crisis.
The Green Party has also accused the government of failing voters on living costs, and campaigned for insulation projects to reduce energy needs and keep homes warm.