Prime Minister David Cameron is "open to all ideas" for returning Royal Bank of Scotland to private ownership but its finances must improve first, he told reporters on the last day of a three-day visit to the United States.
Policy Exchange, the influential centre-right political think-tank, has urged the government to reprivatise both RBS and state-backed rival Lloyds Banking Group through a mass share distribution to the public.
Shares in Lloyds are nearing the price which the government regards as its break-even level, making it more likely it would simply dispose of its 39 percent stake on the open market.
But a public offer looks more of an option for the 81-percent the Treasury holds of RBS, giving it back to taxpayers who would take on remaining risk associated with the bank but profit from any future improvement in its situation.
"In terms of returning RBS to the private sector, involving people in owning this bank in a genuine way, I'm open to all ideas and proposals. But it seems to me the primary question is of getting this bank back into good health," Cameron said.
Britain pumped 45.5 billion pounds into RBS and 20.5 billion pounds into Lloyds to keep them afloat during the 2008 financial crisis. Since then, both banks have undertaken massive restructurings under new management and, bowing to pressure from lawmakers, focused on lending to UK households and businesses.
RBS has shed assets worth around 900 billion pounds ($1.4 trillion) from its bloated balance sheet. There are still hurdles to be overcome, however. The bank said on Tuesday it would need another 18 months to strengthen its capital position enough to satisfy regulators.
"There are connections between the ownership and the health but I think step one is continue the path to health and step two is to think about changing its ownership," Cameron said.
Shares in Lloyds closed on Wednesday at a two-year high of 59.4 pence, just below the 61 pence level which the government regards as its break-even. Shares in RBS closed at 307 pence, meaning taxpayers are sitting on a loss of 17.5 billion pounds.