Chancellor George Osborne was speaking for the Government when he raised questions about continued Greek membership of the euro, Downing Street says.
Mr Osborne told a business conference he did not know whether Greek exit was needed in order to persuade Germany that it must sign up to measures to secure the survival of the single currency.
A Downing Street spokeswoman said that Mr Osborne was expressing views which were "shared" within Government.
But she stressed neither the Chancellor nor Prime Minister David Cameron were predicting Greece's departure from the euro, pointing out that Mr Osborne himself said he did not know whether this would happen.
The Chancellor's comments came just days before the June 17 re-run election in Greece, where the left-wing Syriza coalition is fighting on an anti-austerity platform which some observers believe could force the country out of the euro - something Syriza's leader Alexis Tsipras denies.
Speaking to the conference hosted by The Times in London, Mr Osborne said: "I ultimately don't know whether Greece needs to leave the euro in order for the eurozone to do the things necessary to make their currency survive.
"I just don't know whether the German government requires Greek exit to explain to their public why they need to do certain things like a banking union, eurobonds and things in common with that."
The Chancellor also said the handling of last weekend's 100 billion euro bailout for Spanish banks was "depressing" and "frustrating".
Asked whether the PM shared Mr Osborne's views, a Downing Street spokeswoman said: "These are certainly difficult issues and the Chancellor was setting out views yesterday which are shared.
"It comes back to the basic point that the eurozone needs to stand behind its currency. The Chancellor represents the Government and, being Chancellor of the Exchequer, represents the Government's view."