In a statement released later on Sunday reported by Reuters, the Greek Finance Ministry said Varoufakis was responding to a hypothetical question and that any referendum would "obviously regard the content of reforms and fiscal policy" and not whether to stay in the euro, as Corriere della Sera had suggested.
The comments come ahead of a meeting of euro country finance ministers – where discussions are expected to center on Greece's new action plan to reform its economy and the way it does business.
Read MoreGreece lashes out aspressure to reform rises
Late last month, Greece was granted a four-month extension on its bailout agreement. In return for the deal, which Athens desperately needed to pay its way, the government rolled back on its previous tough anti-austerity stance and pledged to present a series of reforms – including measures to cut down on corruption, tax evasion and change labor laws.
These plans have already made headlines for all the wrong reasons in the last few days, however. On Friday, it was reported that Varoufakis had sent the head of the Eurogroup, Jeroen Djiselbloem, a letter in which he proposed to hire tourists to work as undercover tax inspectors.
Although such a proposal is likely to be met with scepticism in Europe, it demonstrates Greece's efforts to placate its international lenders.
One analyst told CNBC Monday that while Greece was trying to appease lenders, the euro zone was content to let Greece sweat a little before approving its reform plans.
Read MoreIs Greece already rolling back on its pledges?
"The new Greek government is realizing that it has to shift somewhat and is coming up with ideas." Michael Gallagher, director of research at IDEAGlobal, told CNBC Monday.
"But it suits the Europeans to haul the Greeks over the coals because countries like Spain don't want parties like Podemos (a left-wing, anti-austerity party like Syriza) top gain from the politicking in Greece and they don't want this to be the first of a wave of new left-wing governments (in Europe)."