UK Financial Investments (UKFI), the body set up by the government to manage its stakes in the lenders, has invited investment banks to pitch for sale positions.
According to the Financial Times investment banks have until July 8 to submit their proposals.
The government has previously stated its desire to sell down its 82% stake in RBS before the next general election in 2015.
Chancellor George Osborne (pictured) last month also vowed to start selling off its 39% ownership in Lloyds, although the nature and timing of the sale remains uncertain.
The government’s stake in RBS is worth around £14bn and its Lloyds position is approximately £17bn.