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Greece offered a new package of reforms last week in the hope of unlocking remaining funds from its bailout programme, but its EU and IMF lenders have yet to sign up to the proposals.
Athens has not received bailout aid since August last year and has been hard pressed to cover payments amid a cash crunch, resorting to measures such as borrowing from state entities to tide it over.
A source with knowledge of the issue told Reuters last month that Greece had enough funds to last it until April 20.
Varoufakis said on Sunday following a meeting with International Monetary Fund chief Christine Lagarde that Greece intended to meet all obligations to all its creditors, moving to quell fears of a possible default ahead of a 450 million IMF euro loan repayment later this week.
He told the paper the new leftist-led government, confronted with a liquidity squeeze, wanted negotiations to be concluded "as soon as possible" but would not accept terms that suffocated the economy.
"We are not going to condemn the country, as previous governments did, to a long-term asphyxiation," Varoufakis told the paper, suggesting the EU/IMF lenders had treated the previous conservative-led government more leniently.
"The negotiations will end when we reach an honourable agreement, which will give the Greek economy the prospect of real stabilisation and substantive growth," Varoufakis said.