The eurozone's 19 ministers meet in Brussels one day before Greece must make a €750 million debt payment to the International Monetary Fund that some fear the Mediterranean nation cannot afford.
"Unfortunately there is not sufficient progress to reach a decision today, whatever it is," said Germany's powerful finance minister Wolfgang Schäuble as he went into talks with his Greek counterpart Yanis Varoufakis.
Schäuble also raised the possibility of a Greek referendum, saying that "maybe this would be the right measure to let the Greek people decide if it is ready to accept what is necessary."
Led by Germany, the Europeans still expect a rigorous regime of reforms from Athens, but Prime Minister Alexis Tsipras's leftist government, in power since January, has so far refused to deliver.
Eurozone ministers are so far unswayed by the threat of financial catastrophe in Athens and have ruled out imminent compromise to unlock the 7.2 billion euros still owed Greece under its 2012 bailout, which expires at the end of the month.
Greece has had to be bailed out twice since its debt crisis first spooked the markets in 2010, and fears are still high that it could become the first country to crash out of the euro.
Greece sees deal within days
Varoufakis -- whose outspoken stance has won him few friends among his European counterparts -- said he was "very confident" that the meeting would produce a positive statement on Greece's progress.
With no overall deal in sight, Greece is hoping for a nod of approval from the Eurogroup -- the eurozone finance ministers -- that will allow for the last tranche of the bailout to be paid.
The symbolic gesture would also help persuade the European Central Bank to keep emergency funds flowing to Greece's fragile banks.
"There is going to be a communique on the progress we are making and this will be a very good paving stone towards a final conclusion," said Varoufakis, adding that he expected a final deal "in the next few days, I think."
The shaven-headed former economics professor warned however that the Greek government's red lines "by necessity are inflexible - but ours and theirs are such that there is common ground."
Other European leaders were gloomier.
"This meeting won't be conclusive, we all know that," said the EU's Economics Affairs Commissioner Pierre Moscovici.
'Not rocket science'
Ireland's finance minister, Michael Noonan, said that "people are getting concerned including myself about the liquidity situation in Greece."
Slovakia's Peter Kazimir said it the steps Greece needed to take were "not rocket science."
No one outside the Greek government knows for sure how long Athens can go without a deal to end Greece's 240 billion euro bailout, which began in 2010 and expires at the end of June.
Athens faces a harrowing repayment schedule over the coming weeks.
In June alone, Greece owes another 1.5 billion euros to the IMF and it owes another three billion euros to the ECB in July and August.
An official in Athens said the loan repayment due on Tuesday to the IMF will be honoured on schedule.
Greece has been squeezing funds from the central and local governments to be able to meet its payments, but mayors are beginning to resist.
Greek officials went on a frenetic diplomatic offensive last week, with Varoufakis making stops across Europe to drum up support for his beleaguered nation.
Tsipras spoke three times by phone to Europe's most powerful leader, Germany's Angela Merkel, and he repeated calls to Jean-Claude Juncker, the head of the European Commission.
Tsipras, whose Syriza party swept to power on an anti-austerity platform, has called for an "honourable compromise," and the government reportedly plans a number of concessions to win over its creditors.
These include a new VAT rate, along with a restriction on early retirement and an unpopular property tax that would enable the government to save billions of euros as demanded by its creditors.