He told the BBC he could not see who would be willing to put up more loans to bolster Greece's struggling economy.
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.""
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