"Eurozone officials would like a way to say yes to the bond markets, without appearing to let Greece off the hook," said Stephanie Flanders, the BBC's economics editor.
But in public comments at the World Economic Forum in Davos, the EU economic commissioner Joaquin Almunia said the 16-member bloc was not considering a bail-out or a default.
The EU, Spain and Germany have also denied that Greece could be kicked out of the eurozone.
Greek government debt is the world's worst performing in January, according to Bloomberg.
Greek 10-year bonds costs 3.96 percentage points more than German debt - the safest in Europe - on Thursday, the highest since 1998.
The country's finance minister admitted that the nation could not keep paying the kinds of rates it is at the moment.
"It's true that if we service the whole 54bn euros on those terms, it will be pretty disastrous for our ability to do other things," George Papaconstantinou said.
"Well, hopefully we won't have to go on very long doing it."
The prime minister also refused to be drawn in to talk of bail-outs.
"Talking about theoretical possibilities could end up becoming self-fulfilling prophecy," Mr Papandreou said. "Greece is in a situation where we need to take very strong measures and structural changes in our country."
Many observers do not think that Greece will be able to pass its budget, which proposes drastic cuts and huge public sector lay-offs.
There were riots last year, and huge national strikes are already scheduled for the coming months.
'Lesson of history'
EU rules state that no nation in the bloc should have an annual budget deficit higher than 3% of its gross domestic product.
Greece aims to shrink public debt to 9.1% of overall economic output this year, down from 12.7% last year.
Mr Papandreou said in a session at Davos on Thursday that Greece was "being used as the weak link, if you like, of the eurozone".
Our economics editor said that uncertainty about what will happen is making the Greek debt crisis worse.
"The lesson of history - repeated again and again - is that uncertainty about the end-game only brings it closer," she said.
"As we're seeing, "Europe", at times like this, does not speak with one voice."
Greece, Spain, Portugal, Ireland and Italy together account for 40% of the eurozone's debt.
Their debt has ballooned as their countries have been battered by the financial crisis, while larger economies have had to spend huge amounts to bail out their key industries.
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