Greece and Germany may have found a way out of the bailout crisis
The major sticking points that are preventing a deal are things like pensions and labour market reforms, where the Syriza-led government's priorities are most at odds with the rest of Europe.
But if it could be conducted before the country runs out of money entirely, one answer to that might be a referendum on any bailout deal.
There's a big contradiction in Greek public opinion that a referendum would address: The country is strongly anti-austerity and strongly pro-euro.
Despite the incredible economic pain Greece has taken in recent years - on a scale similar to the Great Depression - support for leaving the euro is still low. Polling suggests something like two thirds of Greeks want to stay in the euro.
But something like four fifths of Greeks also want to reject the Memorandum of Understanding (the austerity deal and structural reforms Greece agreed to access bailout funds).
It's quite clear now that these two views are basically incompatible. Syriza was elected on a platform advertising the end of austerity while Greece remained in the euro, suggesting this would be possible to negotiate. In terms of its views on Greece's eye-watering debt burden, Syriza is correct.
But four months after they were elected, it's clear that no other finance minister in Europe agrees with that (publicly, anyway).
A referendum might be a good way to get Greece to weigh up those options, both of which are pretty horrible. Does the country want a bailout deal, and to remain in the euro even if that means further austerity? Or does it want to reject the deal, invite default and go its own way?
Polling so far indicates that the majority of Greeks would take the latter option and accept another austerity package, rather than risk their euro membership. But the same poll suggests that Syriza voters would tip the other way, favouring Grexit if no better deal can be reached.
Bloomberg reported on Wednesday that German finance minister Wolfgang Schaeuble now supports a referendum on Greece's bailout. There's a clear upside for the rest of the Eurogroup - whether Greece chooses the bailout or not, Schaeuble and others can wash their hands and say that they didn't force the country to do anything.
Greek Prime Minister Alexis Tsipras has already promised to hold a vote if he can't negotiate a deal that's consistent with his election pledges.
This is a strange way in which for once, Greece's frustrated European creditors and the government can both win, in a way. The creditors get some closure one way or another, and the Syriza government gets to pass the difficult decision on whether to accept another painful bailout deal to the Greek electorate.
HSBC European economist Fabio Balboni says that it could be a "face-saving strategy to embark on the required U-turn from its pre-electoral pledges."
The vote would take time to organise and could spark major outflows from Greek banks - it's not clear whether it could be done before Greece misses a debt repayment and goes into technical default. But it could give the Greek people a sense of ownership - however brutal - over the decision.