The leaders of Germany and France are set to hold talks in Berlin on whether to give Greece more time to make the cuts required by its debt bailout.
German Chancellor Angela Merkel and French President Francois Hollande will also meet Greek Prime Minister Antonis Samaras later this week.
Meeting Mr Samaras yesterday, eurozone chief Jean-Claude Juncker kept the door open for a change to the bailout terms.
Heavily-indebted Greece is in its fifth year of recession and austerity.
Greece is currently trying to finalise a package of 11.5bn euros (£9.1bn: $14.4bn) of spending cuts over the next two years.
It is also being asked to put in place economic and structural reforms, including changes to the labour market and a renewed privatisation drive.
The measures are needed to qualify for the next 33.5bn-euro instalment of its second 130bn-euro bailout.
The "troika" of donor bodies monitoring the bailout - the International Monetary Fund (IMF), the European Central Bank (ECB) and the European Commission - are due in Athens next month to report on whether Greece has made enough progress.
Greece needs the funds to make repayments on its debt burden. A default could result in the country leaving the euro.
Mr Samaras is seeking an extension of up to two years for the painful steps, in order to provide Greece with the growth needed to improve its public finances.
In an interview published on Wednesday, he told Germany's biggest daily, Bild, that his country needed "a little breathing space" in order to kick-start growth and reduce its deficit.
After meeting Mr Samaras on Wednesday, Eurogroup head Jean-Claude Juncker said a decision on an extension would depend on the troika's report.
"We have to discuss the length of the period and other dimensions," Mr Juncker told a news conference, while sitting alongside Mr Samaras.
He said Greece was facing its "last chance" to make the necessary changes, but praised the "tremendous efforts" it has made so far to cut its deficit. He also stressed he was "totally opposed" to Greece leaving the euro.
Mr Samaras called the discussions "fruitful".
At least publicly, many EU leaders remain resolutely opposed to any moves to change the terms of Greece's bailout.
But Mr Juncker's remarks suggest there is room for manoeuvre and that an extension has not been ruled out, says the BBC's Stephen Evans in Berlin.
Mrs Merkel has said that she and Mr Samaras will not make any decisions on the issue in their talks on Friday. Mr Samaras goes on to meet Mr Hollande on Saturday.
On Wednesday, Mr Hollande also discussed Greece with British Prime Minister David Cameron in a telephone call.
"Both welcomed the recent actions of the ECB and agreed that this did not negate the need for Greece to stabilise their own economy and prevent any further detrimental effects to the wider eurozone," Mr Cameron's office said in a statement, without specifying which ECB actions they were referring to.
The talks come amid reports that due to the worsening state of the economy, which affects tax receipts and welfare spending levels, Greece may now need to find savings of up to 13.5bn euros - 2bn more than thought.
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