In an interview with the German Die Welt newspaper, the Chancellor said that he very much wanted the UK to continue as an EU member state.
However he made clear that in order for that to happen, there would have to be meaningful reform of the current arrangements.
"I very much hope that Britain remains a member of the EU. But in order that we can remain in the European Union, the EU must change," he said.
A Treasury aide insisted that his comments were fully consistent with the Government's position - that the EU needs to change "and indeed is changing".
However the fact such a senior member of the Government is prepared publicly to discuss the possibility Britain may be unable to stay in the EU is likely to be welcomed by Tory eurosceptics who have been pressing for an in-out referendum on Britain's membership.
Osborne made his comments during a visit to Berlin on Tuesday. On Thursday a key ally of German chancellor Angela Merkel issued a sharp warning that any attempt at "blackmailing" member states into accepting change would backfire on Britain.
Bundestag European affairs committee chairman Gunther Krichbaum said a referendum could leave the UK isolated in Europe.
"You cannot create a political future if you are blackmailing other states. That will not help Britain," he said.
Earlier this week Sir Richard Branson teamed up with top businessmen to caution David Cameron his plans to renegotiate the UK's relationship with the EU could harm Britain's economy, and the US assistant secretary for European affairs, Philip Gordon, has made clear the Obama administration wanted "a strong British voice" in the EU and referendums risked turning countries "inward".
Downing Street said today that David Cameron had talked Barack Obama through Britain's approach to Europe when they spoke before Christmas and that the president was supportive.
Shadow foreign secretary Douglas Alexander said George Osborne's real audience was not Die Welt but "Conservative backbenchers."
“No wonder only this week Britain’s allies and British business leaders warned the Government about the risk of sleepwalking to exit.
“As this week has shown Cameron and Osborne are neither in control of their party nor the agenda," he said.
Cameron is due to spell out his position more fully in a keynote speech later this month, where according to The Sun he will promise British voters an in/out referendum in 2018 if the Conservative Party is returned to power at the next election.