Greece's creditors have said the country has until Friday to request an extension to the 240 billion euro bailout that has kept Greece afloat since 2010 and whose main component expires on Feb. 28.
But the new government in Athens, elected last month on a promise to renegotiate the bailout's harsh spending cuts, has been adamant it cannot seek to extend a program it believes is wrong. Instead, Athens says it is preparing a request to extend its loan agreement, but not the austerity budget measures that accompanied the bailout.
The divide has threatened to scuttle negotiations and increased the risk of Greece having to leave the eurozone, raising concern among European governments and global markets.
"I want to believe that (the negotiations) will end well tomorrow, the day after tomorrow," Varoufakis said as he left Parliament Wednesday night. "We are on a good path. The negotiations are showing all the signs of convergence."
However, he said, "until we reach a result, nobody can be certain."
Varoufakis said the extension request "will be written in a way that covers both the Greek side and the president of the Eurogroup," referring to Dutch Finance Minister Jeroen Dijsselbloem, who heads the meetings of eurozone finance ministers.
Germany, the main European creditor, expressed deep skepticism when Athens initially said it would ask for a loan agreement extension Tuesday night. The European Commission said it would like to see what the proposal entailed before offering support.
The United States has urged Athens and European lenders to swiftly resolve their differences.
Both sides agree Greece needs external support to keep it afloat and buy time for more thorough talks. But Athens rejects the eurozone's request that it continue the budget austerity cuts.
Amid the high tensions, U.S. Treasury Secretary Jack Lew spoke on the telephone with Greek Finance Minister Yanis Varoufakis. He "noted that failure to reach an agreement would lead to immediate hardship in Greece, that the uncertainty is not good for Europe, and that time is of the essence," according to a Treasury Department statement.
Earlier this week, Varoufakis told his eurozone counterparts that Greece was ready to apply for an extension of the loan agreement and also agree on "a number of sensible conditionalities" during that period. He did not elaborate, however, on what they might be, according to a transcript of his speech released by the ministry.
Analysts say Greece's proposal improves the odds a little for a deal, but a large snag is that the government still rejects the budget terms attached to the loans.
Holger Schmieding from Berenberg Bank singled out Athens' desire to reverse a series of structural reforms, such as raising the minimum wage back up.
That, he said "does not come close to what creditors could accept."
Fitch ratings agency said the onus is on Greece to compromise.
"Our base case remains that the incentives to reach a negotiated agreement are sufficiently strong, but the risks of a policy mistake on either side have risen," it said, warning the current uncertainty could derail Greece's incipient economic recovery.
German Finance Minister Wolfgang Schaeuble was openly skeptical, even referring to the possibility of Greece having to leave the euro if it does not accept the eurozone's conditions.
"We're a bit used to this — every day there are different reports, and then when we are in a room together things sound completely different," he said told ARD television Tuesday night.
The European part of Greece's bailout expires on Feb. 28. If no deal is reached by then, the European Central Bank would face increased pressure from eurozone governments to cut off emergency financing for Greek banks.
That could place so huge a strain on the country's financial system that the government might be forced to print its own currency and leave the euro. That's a worst-case scenario for all sides — Greece's economy would suffer terribly, at least in the short term, and European countries could be stuck with losses on their loans to Greece.
"No one in the eurogroup wants to force Greece out of the euro," Schaeuble said. "It's entirely up to officials in Greece."
Geir Moulson in Berlin, Lorne Cook in Brussels, David McHugh in Frankfurt, Germany and Martin Crutsinger in Washington DC, contributed to this report.