Yannis Stournaras said: “If there is need for further support to Greece, it will be in the order of about 10 billion euros [$13.4 billion], or much smaller than the previous programmes.”
Greece has already received two bailouts totalling about 240 billion euros.
Meanwhile, Cerman Chancellor Angela Merkel has warned about writing down any more Greek debt.
She said a so-called haircut of Greek debt would be bad for the stability of the eurozone, which has seen a return in investor confidence after years of worrying about the future of the single currency following bailouts of several nations – most recently, Cyprus.
“I am expressly warning against a haircut,” Angela Merkel said.
“It could trigger a domino effect of uncertainty with the result that the readiness of private investors to invest in the eurozone again falls to nothing.”
Angela Merkel’s comments come after Germany’s finance minister, Wolfgang Schaeuble, said – for the first time – earlier this month that Greece will need another bailout to plug a forthcoming funding gap.
The issue of bailouts is a sensitive one in Germany, where Angela Merkel faces elections for a third term on September 22.
Many Germans feel they have already contributed enough to European bailouts.
The International Monetary Fund (IMF) last month estimated Greece would need around 11 billion euros in 2014-15.
On Sunday, Yannis Stournaras told Greek newspaper Proto Thema that any further bailout would be smaller than the previous two.
But he also warned that Greece would not accept any more forced spending cuts from its partners.
“We are not talking about a new bailout but an economic support package without new [austerity] terms… until 2016, the targets – our obligations – have been set and other measures or targets cannot be required.”
The Greek economy has shrunk further than any other in Europe, with bailout money only released on condition that the government imposes cuts and implements restructuring.
It comes after most of the 18-member eurozone countries came out of recession earlier this year.
Greece’s troika of lenders – the European Commission, the European Central Bank and the IMF – will review the aid programme in the autumn.
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