Angela Merkel and Francois Hollande will also meet Greek Prime Minister Antonis Samaras later this week.
Meeting Antonis 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 finalize a package of 11.5 billion euros ($14.4 billion) 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 labor market and a renewed privatization drive.
The measures are needed to qualify for the next 33.5 billion-euro installment 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.
Antonis 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 Antonis 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,” Jean-Claude Juncker told a news conference, while sitting alongside Antonis 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.
Antonis 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 Jean-Claude Juncker’s remarks suggest there is room for manoeuvre and that an extension has not been ruled out.
Angel Merkel has said that she and Antonis Samaras will not make any decisions on the issue in their talks on Friday. Antonis Samaras goes on to meet Francois Hollande on Saturday.
On Wednesday, Francois 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 stabilize their own economy and prevent any further detrimental effects to the wider eurozone,” David 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 13.5 billion euros – 2 billion more than thought.
Greece discussions timetable
• 22 August: Greek PM Antonis Samaras meets Eurogroup chief Jean-Claude Juncker
• 23 August: Angela Merkel and Francois Hollande meet
• 24 August: Chancellor Merkel and PM Samaras meet
• 25 August: President Hollande and PM Samaras meet
• Early September: Troika staff go back to Greece
• 14-15 September: Gathering of European finance ministers in Cyprus
• Troika’s review of progress to be published by the end of September
• 8-9 October: Finance ministers attend two days of meetings in Luxembourg
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