Royal Bank of Scotland Group PLC, Britain's biggest government-owned bank, may use surplus capital to buy back part of the taxpayers' stake, said two people with knowledge of the situation.

RBS and the government are considering the proposal after the bank's shares rose recently, giving the Treasury a paper profit on its stake, said the people, who declined to be identified because the talks are private. The U.K. may also sell part of its $70 billion stake in Edinburgh-based RBS to money managers, the people said.

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