U.K.-government owned Royal Bank of Scotland said it wanted to start writing the sale prospectus for investors in mid-2014 or earlier after announcing its first quarterly profit in 18 months.
The Edinburgh-based bank reported a profit of 826 million pounds ($ 1.25 billion) for the first quarter, compared with a 1.5 billion pound loss the same time last year.
(Read More: UK Banks Return to Favor in Turnaround Year)
The bank's chairman, Philip Hampton, said RBS could be ready for sale from the middle of 2014 – or even earlier.
"It could be earlier, that's a matter for the government. But we think the recovery process will be substantially complete in about a year or so's time," said Hampton
.Hampton's comments were made on a video statement along with the results. The news sent shares 4 percent lower in morning trading.
RBS was bailed out by the U.K. government and is currently 82 percent owned by U.K. taxpayers.
Stephen Hester, RBS chief executive, said: "Privatisation would be a terrific thing for the country, both psychologically and in terms of taxpayers' money being freed up for other uses."
On Thursday, the Financial Times reported U.K. finance minister George Osborne's allies were considering selling the government's majority stakes in RBS and another U.K. bank Lloyds, even though the share prices of both banks are below the level the government paid for them.
(Read More: Osborne Allies Ready to Sell Bank Stakes Before GeneralElection)
RBS shares traded at 292 pence on Friday morning, whereas the government bailout price was 500 pence.
—By CNBC.com's Jenny Cosgrave; Follow her on Twitter