The Greek government is fast running out of money and is due to make a payment of €1.5 billion ($1.7 billion) to the International Monetary Fund (IMF) on June 5.
Yanis Varoufakis told Star TV a deal with creditors was “very close” and denied Greece might leave the eurozone.
“Another currency is not on our radar,” he said.
PM Alexis Tsipras also talked up the prospect of a deal in a speech to Greek business figures earlier, saying the government was “in the final straight” before a deal.
Greece has been locked in negotiations with the EU and IMF over economic reforms they say must be implemented before the final €7.2 billion tranche of the country’s €240 billion bailout is released.
Issues over pension reform, taxation, deregulation of the labor market, and the re-hiring of 4,000 former civil servants are yet to be resolved.
Last week, the government emptied its IMF reserves in order to pay €750 million in debt interest on its existing loans.
An apparent proposal from European Commission President Jean-Claude Juncker emerged in Greek newspaper To Vima on May 18 before a spokeswoman quickly said she was unaware of it.
However, the plan for emergency funding and smaller primary surplus targets, in return for limited Greek fiscal reforms worth €5 billion, was not completely denied.
A Commission spokeswoman said she was unaware of Jean-Claude Juncker’s reported proposal.
The status of Jean-Claude Juncker’s proposal was unclear, but European Economic Affairs Commissioner Pierre Moscovici complained in Berlin that the left-led government was “more eager to say what they don’t want to keep in the program than to propose alternatives”.
Greek media reported on May 19 that the government had sent proposals to its international creditors to revamp VAT rates in an attempt to tackle tax evasion.
Alexis Tsipras is due to attend the EU Eastern Partnership Summit in Riga, where Greece is likely to be a key topic.
Yanis Varoufakis said a payment deal was on the cards, but insisted he would reject any compromise he considered “non-viable”.
European Commission spokesman Margaritis Schinas has welcomed the commitment by the Greek government to bring the talks to a conclusion, but said more time and effort was needed “to bridge the gaps on the remaining open issues in the negotiations”.
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