Eurozone finance ministers will meet later today where it is expected they will decide on whether to extend or end the Greek bailout deal.
The newly-elected Syriza party does not want an extension - saying the terms of the bailout are crippling the Greek economy.
Yesterday, around 15,000 people took part in a mass rally outside the Greek parliament in Athens against austerity measures imposed on the country.
The new prime minister of Greece has said he is hopeful a debt deal can be agreed to keep the country in the Euro.
Alexis Tsipras and his finance minister have met with head of the Eurogroup Jeroen Dijsselbloem, to try to hammer out technical details of a compromise.
European leaders have agreed to extend talks about the debt crisis, to resolve the impasse since the Syriza-led government took power last month.
Greece and Germany are said to be discussing a deal which is likely to involve a continuation of the Greek bailout, with fewer conditions as currently imposed.
Germany is willing to loosen some of the austerity and provide financing that will support the public sector and keeps banks afloat.
Backroom negotiations have been continuing ahead of the meeting today.
Newstalk.com's Shona Murray is in Brussels.
Dr Eoin Drea is an economist and research officer at the Martens Centre for European Studies in Brussels. He says if no deal is struck today Greece may need to negotiate a completely new bailout.
Speaking after a meeting last week, Taoiseach Enda Kenny said the aim is to find a basis from which to go forward.