The UK government may begin an initial sale of shares in Royal Bank of Scotland (RBS) in September 2015 to avoid clashing with the sale of Lloyds Banking Group.
The full privatisation of Lloyds Banking Group will begin in March 2016, local media report suggest.
The government will consider launching a sale of shares worth between £3bn and £5bn initially to institutions such as pension funds and insurers to boost liquidity in the stock.
However, the British government has not yet finalised any decision.
"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’," Reuters quoted a senior fund manager as saying.
"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."