But he said he hoped the process of returning £45 billion to the public purse could be started in the years after the 2015 General Election.
In 2008, as the financial crisis struck, the UK Government decided to use taxpayers' money to save the Edinburgh-based institution rather than see it collapse, spread consumer panic across the High Street and lead to runs on other banks.
As well as stumping up £45bn to save RBS, the Treasury also bailed out Lloyds Banking Group to the tune of £21bn; a total of £66bn.
Originally, it was suggested the Coalition wanted to sell off the public's 81% share in RBS and 39% share in LBG before the 2015 General Election.
It has already begun the process of selling back to the private sector LBG; last September it sold 6%, raising £3.2bn. Asked if taxpayers would get all their money back, Mr Alexander said: "We will but it is a long haul."