The emergency meeting of the single currency zone's finance ministers is the first since the radical-left Syriza party won the general election in Greece last month on a pledge to drastically reduce the burden of the country's bailout and the associated budget austerity measures.
Popular support for a change of course is strong in Greece, with thousands taking to the streets across the country Wednesday to give their backing to the government. Greek police say about 15,000 people attended a rally in Athens' central Syntagma Square. Another 5,000 gathered in the northern city of Thessaloniki.
Since winning the Greek general election last month, the Greek government has outlined its broad ambition but it has still to present concrete proposals. Varoufakis has said he wants to scrap Greece's current bailout program and agree on a new one.
That would take time, though, and Greece's current bailout program ends after Feb 28.
Without the bailout's financial support, Greece faces bankruptcy and a possible exit from the eurozone, a development that could further damage Greece's economy, at least in the short-term, and throw global financial markets into turmoil.
"I'm confident we are going to have a very constructive meeting," Varoufakis said.
So far, eurozone officials have yet to embrace the idea of a new bailout deal.
Jeroen Dijsselbloem, who chairs the meetings of eurozone finance ministers, promised to listen to Greece's plans but suggested a conclusive deal was unlikely on Wednesday. The finance ministers will meet again Monday.
German Finance Minister Wolfgang Schaeuble agreed that a deal Wednesday was unlikely and that the meeting would be an opportunity for both sides to define "red lines."
The new Greek government won elections last month on a mandate to get concessions from Greece's creditors, which also includes the International Monetary Fund. The IMF's managing director, Christine Lagarde, was also at the meeting as was European Central Bank President Mario Draghi.
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