The unexpected meeting would be "an informal discussion" on Greece's reform plan, the finance ministry and the IMF said. Varoufakis is also expected to meet US Treasury officials on Monday.
Greece is fast running out of cash and its euro zone and International Monetary Fund lenders have frozen bailout aid until the leftist-led government reaches agreement on a package of reforms.
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Greece has not received bailout funds since August last year and has resorted to measures such as borrowing from state entities via repo transactions to tide it over.
After a first set of planned measures failed to impress lenders, Athens sent a more detailed list to institutions representing the creditors - the European Commission, the European Central Bank and the IMF - on Wednesday.
But the list arrived too late to be discussed by euro zone deputy finance ministers - the Euro Working Group that usually prepares meetings of euro zone finance ministers who can decide whether to grant new loans to Greece - at a teleconference on Wednesday afternoon.
EU officials have said that progress had been made in talks but more work was needed for a deal to be reached.
"It is necessary to restore the Greek economy's funding flow," Labor Minister Panos Skourletis told Greek Ependysi newspaper, accusing the country's lenders of taking advantage of Greece's funding limits to add pressure on Athens.
"Whether the country will meet its external obligations depends on our lenders' final political choices and stance," he said, adding that pensions and wages were not at risk.
Greece has its hopes set on another meeting of euro zone deputy finance ministers on the afternoon of April 8 and on the morning of April 9, although it is unlikely that a deal could be reached by then. The next meeting of euro zone finance ministers will take place on April 24 in Riga.
On April 8, Greek Prime Minister Alexis Tsipras will meet Russian President Vladimir Putin in Moscow. It will be his first visit to the Russian capital since taking office in January.
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