British Gas owner Centrica is considering offering free power to customers on Saturdays to encourage energy use when overall demand is low.
As part of a shake-up in the way energy is used and paid for, free energy tariffs could be offered to those who have a 'smart meter' installed in their homes.
British Gas has fitted over a million of the devices, which detect how much power is used on each day, in UK properties so far.
The offer would apply to homes and not businesses and to electricity use, not gas.
The proposals mirror tariffs already available to US customers of Direct Energy, the sister company of British Gas in North America.
A Centrica spokesman told Sky News: "In Texas, we had a product called 'free power Saturdays'. A fairly simple idea, free power on a Saturday.
"The thinking behind it is for customers to concentrate energy use when demand is low, to reduce demand in the week.
"We are looking to do that over here, we've been thinking about it for a while. A small trial is running at the moment."
He said the scheme would only work for homes that have a smart meter, which would allow Centrica to know when electricity is being used, including whether it is being used on a Saturday.
"This is in the very early stages. It could be in place by mid next year, hypothetically," he added.
The move is likely to be seen as a reaction to political pressure on the UK's 'Big Six' energy suppliers to cut bills and ensure customers are getting the best deals as Britons struggle to cope with the rising cost of living.
Sam Laidlaw, chief executive of Centrica, told the Financial Times: "We need to get more smart meters in the UK, and if it (free power days) does come to the UK it will be at least six months."
The announcement came just hours after British Gas announced profits for its residential energy business in the six months to the end of June grew by 3.2% to £356m.
The company has insisted that it did not cash in on the bitterly cold start to the year, despite gas consumption rising by 13%. It defended the rise in profits, saying they were curtailed by "significantly higher environmental and commodity costs".