In an interview with the German newspaper Welt am Sonntag, Hester said he would be “disappointed” if ministers did not begin the process of selling down the Government’s 83% stake in 2011.
He added the share sale “won’t be conducted in one go”.
RBS beat expectations with a return to profit in the first three months of the year. It has raised more than £1.64bn from exiting or selling more than 20 businesses over the past year.
Hester said the bank will leave all the areas where it cannot establish itself among market leaders.
It is also selling some of parts of ABN Amro which it bought in 2007, a transaction Hester said was “clearly a big mistake”.
Hester reiterated his goal of ensuring RBS has a double-A credit rating by 2013.