The energy firm wants to cut demand on weekdays and has plans in place to offer the free power deal to their customers from the middle of next year.
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 trialled it, if it works then we could potentially offer it as a product for customers from the middle of next year."
One million homes in the UK 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.