The Chancellor said he was looking at hiving off weaker parts of the state- controlled firm into a "bad bank".
He told the Daily Telegraph the issue was "top of his in-tray".
"We are looking at the case for a bad bank and, if not a bad bank, what is the alternative strategy that really gets on top of the problems in that bank and goes on being what I want it to be which is a bank supporting the British economy," Mr Osborne said.
However, he stressed the Government was not currently "close to the stage of being able to sell RBS shares".
"RBS was a much more complex bank," he said. "To be fair to management past and present, it was a bank that was in a lot more trouble."
Mr Osborne also said he was considering offering state-owned shares in Lloyds to the general public.
"We are now looking actively at a retail offer for the next tranche of Lloyds shares," he said.
© 2013 Press Association