The tariff under consideration is intended to cut weekday demand peaks by encouraging customers to use electricity-hungry appliances, such as washing machines, at the weekend.
Centrica has already introduced the concept of free-power Saturdays in the US, through retail arm Direct Energy.
Customers would need a smart meter to take up the tariff. British Gas has installed more than 1 million smart meters for UK homes and businesses.
Sam Laidlaw, chief executive of Centrica, told the Financial Times: “We need to get more smart meters in the UK, and if it does come to the UK it will be at least six months.”