The report, which cited sources close to the process, said this possible RBS stake sale would target institutional investors and sovereign wealth funds in the Middle East and Asia.
Officials at the British Treasury could not be immediately reached for comment on the report.
The government accumulated stakes of 83 percent in RBS and around 40 percent in Lloyds after bailing out both banks with billions of pounds of taxpayers' money during the credit crisis.
The Conservative-Liberal Democrat coalition government wants to sell back those stakes to the private sector, raising cash to cut Britain's deficit, but has said any sales are unlikely until the Independent Commission on Banking (ICB) publishes a final report on the sector in September.
The commission said in an interim report last month Britain's top banks should shield retail operations from riskier investment banking activities and should boost capital levels to protect taxpayers from future crises.
Qatar's Prime Minister Sheikh Hamad bin Jassim bin Jabr al-Thani said in February Qatar was open to buying stakes in RBS and Lloyds and had discussed investing in the UK.
RBS Chief Executive Stephen Hester said earlier this month any disposal of the UK's RBS stake remained some way off.
"I don't believe it (the government) is preparing anything with a definitive eye ... We've had no conversations with investors, specifically, with this in mind," he said at the RBS first-quarter results presentation.