The first tranche of shares in RSB may be sold off in September, netting up to £5 billion for the UK Government.
The month is being earmarked by Treasury officials who are keen to avoid a clash with the full privatisation of Lloyds Banking Group in March, according to a senior source.
The Edinburgh-based bank was rescued by the Labour Government in 2008, at a cost of £45 billion pounds to taxpayers. Taxpayers have an 80 percent stake.
The source said the Treasury and UK Financial Investments (UKFI), which manages the stake, are examining the possibility of a first sale of RBS shares in the autumn.
It would net between £3-5 billion for the government.
A decision has yet to be taken, but Chancellor George Osborne wants initially to sell several billion pounds worth of RBS shares to institutions such as pension funds and insurers.
The move would boost liquidity in the stock and make it more attractive to future investors.
"There's going to be an RBS sale quicker than everyone thinks. It may take Lloyds by surprise, because they looked 'next in the queue'," a senior fund manager told Reuters.
"The thinking from the Treasury and UKFI is a sale may happen at a loss. UKFI's charter is to maximise value as they see fit. They can't just sit there and wait for 'break-even' or 'above', that might not happen for long time," the fund manager added.
Officials are aware the move cannot coincide with plans for a final sale of shares in RBS's bailed-out rival Lloyds which will also see billions of pounds worth of shares sold including to retail investors.
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