The energy firm has announced plans to trial the initiative and could make it available to customers by mid-2014.
Centrica already offers a Free Energy Saturdays tariff to customers in the US.
A spokesman for Centrica said: "Our North American business offers a product for those customers in Texas who have a smart meter.
"We are looking to see whether we can introduce it into the UK for customers with a smart meter.
"Once we have trialed it, if it works then we could potentially offer it as a product for customers from the middle of next year."
One million UK homes and businesses already have smart meters installed, which automatically send readings to British Gas.
Centrica hopes the scheme will encourage households to use electrical appliances at the weekend, when industrial demand is lower.
The development came as Centrica hinted at further price rises as British Gas announced profits from its residential arm rose by 3.2% thanks to the freezing spring weather.
Revenues from household supply of gas were up 16% to £3.7 billion, compared to the same period in 2012, as Britons cranked up the thermostats. Average residential consumption by volume was up 13% for gas and 1% for electricity.
Operating profits at Centrica were up 9% from £1.45 billion to £1.58 billion. The results sparked anger and calls for British Gas to keep a lid on tariffs.
Its profits would have been higher but were held back by a new duty to pay for energy efficiency measures in customers' homes, which helped push environmental costs up 37% for the period.
Centrica warned that the scheme, which has landed it with a £1.4 billion bill, would "inevitably impact on customer bills ultimately" and that it was facing "upward pressure on costs".
Finance director Nick Luff said: "We will keep prices as low as we can for as long as we can. If prices do have to go up, we will delay it for as long as possible."
He defended the £11 million increase in profits for British Gas residential energy supply, saying it represented just 70p per customer. The company serves more than 11 million households, with nearly 16 million customer accounts.
It pointed out that its profit margin for the residential business fell from 7.2% to 6.5%, meaning it was making less money as a percentage of its revenues and only increased profits this time because of the unusual weather.
Chief executive Sam Laidlaw said: "With our customers using more gas to stay warm during the unusually cold winter, we're doing everything we can to help them keep their energy costs under control and make bills simpler and clearer."
But Len McCluskey, general secretary of the Unite union, said: "These profits will anger a growing number of families who are struggling to pay the bills, made worse when the fuel companies hiked their charges last year.
"There should be a commitment from British Gas and the other fuel providers, all of whom have done very well out of the British people, to cut prices for customers this coming winter."
Mike O'Connor, chief executive of Consumer Futures, called for Centrica to keep a lid on prices after benefiting from the cold weather.
He said: "Wholesale gas prices have not risen significantly and their gas production and much of their generation business has done well. Those factors should give British Gas confidence to hold its prices."
Centrica's announcement comes days after MPs warned of deep distrust in energy firms over tariffs and profits. Yesterday, French-owned rival EDF announced its profits had risen to a record £903 million in the wake of the cold spell.
Elsewhere in the results, the company said it had added 56,000 British Gas residential energy accounts and added more than a million smart meters in UK homes and businesses.
During the period, Centrica bought a 25% stake in the Bowland shale exploration licence in Lancashire operated by Cuadrilla.
It described shale as a potentially important source of gas for the UK. Mr Luff said the company would work with local communities to address any concerns about such projects - in the wake of protests at a Cuadrilla site in West Sussex.
Centrica also said a recent announcement that its Direct Energy arm had bought the New Jersey based Energy Marketing business of Hess Corporation for £478 million meant it was now the largest business gas supplier on the US East Coast.
The company also said it had increased profitability in its international gas and oil production business.