The scheme, proposed by National Gas, would be similar to that run last winter for electricity - where households received discounts on their bills for cutting usage when capacity was low.
The Demand Flexibility Service (DFS) was brought in last year over fears of a shortage of electricity. As NimbleFins previously reported, the DFS will run again this year.
National Gas, which runs the UK's main gas network, said the UK's gas supply was in "a better position" this year, but was looking at ways to bring the cost of gas down for customers.
The scheme, which is currently a proposal, would see households in England, Scotland and Wales sign up to use less gas at peak times to receive a discount on their bills. Early evening is the most likely time the scheme would run.
A spokeswoman told the BBC: "We are in the early stages of exploring whether a small-scale trial could look at the feasibility of the public turning their gas down slightly during times of reduced supply - voluntarily and in return for payment.
"We are in a better position this year in terms of gas supplies, but it's important we look at a range of long-term options to bring down costs for consumers and balance supply and demand."
The UK gets half its gas from Norway. Although gas has been stored in the run up to winter, a cold snap in Europe could still disrupt supplies, according to National Gas.
The energy crisis started after the pandemic when demand rapidly escalated as countries returned to normal.
But it was made worse after Russia's invasion of Ukraine, as mainland Europe was heavily dependent on Russian gas. Europe wanted to reduce its Russian imports, while Russia also made exports difficult, sparking a surge in the price of energy as supply vanished.
Electricity bill discount returns
The Demand Flexibility Service is returning in 2023/2024 to give households the opportunity to earn discounts on their electricity bill if they cut usage at peak times.
National Grid ESO, which operates the main electricity network, said the scheme would be open to even more people and businesses this year after 1.6 million took part last winter.
As NimbleFins previously reported, the "tight days" where electricity capacity is low, were likely to be in January.
However, it has said the chance of blackouts is lower than last winter, with capacity forecast to be slightly better.
Last winter 3,300 megawatt hours (MWh) were saved across 22 DFS days, which was enough to power 10 million homes, National Grid ESO said.