Greece wants to re-negotiate its bailout, but Mr Greenspan said "I don't think it will be resolved without Greece leaving the eurozone".
Earlier, UK Chancellor George Osborne said a Greek exit would cause "deep ructions" for Britain.
Mr Greenspan, chairman of the Federal Reserve from 1987 to 2006, said: "I believe [Greece] will eventually leave. I don't think it helps them or the rest of the eurozone - it is just a matter of time before everyone recognises that parting is the best strategy.
"The problem is that there there is no way that I can conceive of the euro of continuing, unless and until all of the members of eurozone become politically integrated - actually even just fiscally integrated won't do it."
Following the election in Greece of the anti-austerity Syriza party, Greek ministers have been touring European capitals trying to drum up support for a re-negotiation of its bailout terms.
However, there appears little willingness in Berlin, or at the European Central Bank, to alter the terms of its €240bn (£182bn) rescue by the European Union, ECB, and International Monetary Fund.
"The [bailout] conditions with Greece were generous, beyond all measure,'' German Finance Minister Wolfgang Schaeuble said last week. He saw no justification for relaxing them further.
Mr Greenspan said: "All the cards are being held by members of the eurozone."
He also warned that trying to hold the 19-nation euro bloc together "is putting strain on everybody". He said as well as Greece leaving the eurozone, there was a real risk of a "much bigger break-up" with other southern European countries forced out.
Earlier on Sunday, Mr Osborne told the BBC's Andrew Marr Show that the UK was stepping up contingency planning to prepare for a possible Greek exit.
"This stand-off between Greece and the eurozone is increasing the risks every day to the British economy," the chancellor said.
A Greek exit from the single currency would create instability in European financial markets and cause "real ructions" in Britain, too, he added.
Greece's prime minister Alexis Tsipras wants to put in place a short-term financial plan enabling the country to pay its way while it renegotiates the austerity cuts and conditions attached to its bailout terms. The existing bailout ends on 28 February.
Later on Sunday, Mr Tsipras is due to make his first major speech to parliament since taking over as prime minister.
Reports say that, as well as updating the country on the progress of talks with European ministers and policymakers, he is likely to repeat his pledge to increase the minimum wage and provide free electricity for poorer Greeks.
Mr Tsipras is to meet EU leaders at a summit in Brussels on Thursday. Mr Varoufakis will meet eurozone finance ministers the day before.