But the Chancellor offered no timetable or price for share sales and said that the sale of the Government's stake in the Royal Bank of Scotland remains "some way off".
In his annual Mansion House speech in the City of London, Mr Osborne said he has ordered an urgent review, to report in the autumn, into the possibility of breaking up RBS into a "good bank" and a "bad bank", to separate out toxic assets and risky loans from parts of the business which support the economy. The review will particularly focus on assets in Ulster Bank and UK commercial real estate, and will not involve any further injection of taxpayer money into RBS.
The first sale of Lloyds shares is likely to go to institutional investors, said the Chancellor. But he said he was considering a retail offering to the general public for later tranches, raising the possibility of a "Tell Sid"-style privatisation of the kind seen in the 1980s.
In some of his most upbeat comments about the state of the UK economy since the start of the downturn, Mr Osborne said Britain had "left intensive care" and was now "moving from rescue to recovery". And he told his audience of City figures: "Nothing better signals Britain's move from rescue to recovery than the fact that we can start to plan for our exit from Government share ownership of our biggest banks."
He set out three objectives that will guide the Government's approach on the banks, saying it must maximise their ability to support the UK economy, get the best value for money for the taxpayer and do whatever can be done to return them to private ownership.
The Government bought 39% of Lloyds shares and 81% of RBS in a multi-million pound bailout at the height of the financial crisis in 2008, and speculation has been mounting that the Treasury wants to begin the process of selling its stake before the 2015 general election. Prime Minister David Cameron recently raised the prospect of selling RBS shares at a loss.
Mr Osborne today said that Lloyds was now in a "good position" with growing investor interest and shares trading at "around the price where selling would reduce the national debt".
The Government believes a sale price of 61.2p would allow it to recoup the £20 billion it ploughed into the bank. Shares today closed down 0.42p at 61.76p.
Mr Osborne, who was pictured using a cashpoint at a Lloyds TSB bank in London's Strand earlier, said: "I can announce that we are actively considering options for share sales in Lloyds. Of course, we will only proceed if we get value for the taxpayer. And we have no pre-fixed timescale or method of disposal.
"For the first block of Government shares, an institutional placement is likely to be the most effective way of managing risk and getting value. So five years on from the financial crisis, we can now take the first steps to returning Lloyds to the private sector where it belongs.
"And for later sales of shares, we will consider a retail offering to the general public."
By contrast, Mr Osborne said there was "no doubt" that RBS remains "weighed down by too many poor assets", including loans issued in the pre-2008 boom which have since gone bad.
And he poured cold water on expectations of a sell-off at a loss by saying: "I don't want a quick sale of our RBS shares. I want the right sale - the right sale for the British people.
"I will only sell our stake in RBS when we feel the bank is fully able to support our economy and when we get good value for you, the taxpayer. In our judgment, when it comes to RBS that moment is some way off."
With hindsight, it might have been better for RBS to have been split into good and bad banks in 2008, said Mr Osborne, though he stressed he was not seeking to criticise the decision of his predecessor as chancellor Alistair Darling, who "had to act quickly in a desperate situation".
He said he has ordered a swift review, conducted by the Treasury with external professional support, into the merits of breaking the bank up now.
"We will urgently investigate the case for taking the bad assets - those mistakes of the past - out of RBS," he said. "We will judge whether this will allow the Bank to focus on its future supporting the British economy. We will see whether it's right for Britain to, in effect, see RBS broken up...
"We'll look at a broad range of RBS's assets, but particularly assets in Ulster Bank and UK commercial real estate.
"We're not prepared to put more taxpayer capital into RBS as part of this process. We will establish a bad bank if it meets our three objectives: if it supports the British economy; if it's in the interests of taxpayers - and if it accelerates the return to private ownership.
"But if the review reveals that it would not achieve these things, then we won't do it."
Mr Osborne also announced that a market review of small business banking launched today by the Office of Fair Trading will include an assessment of the impact that the sale of Lloyds and RBS branches to new "competitor" banks will have on competition in the sector.
And more broadly, he warned that risks remain to Britain's economic recovery, including the "fragile" state of the eurozone, high debts at home and recent volatility in financial markets.
"Let me say tonight: the British economy is healing," said Mr Osborne. "We are moving from rescue to recovery. But while Britain has left intensive care, we still need to secure the recovery - and make sure we continue to treat the ailments that brought us low in the first place. Full recovery won't be easy but I won't let up in my determination to put right what went so badly wrong."