Speaking on ZDF television late on Thursday, Deutsche Bank chief executive Josef Ackermann said he was “doubtful whether Greece will really be in a position to achieve" the repayment of the emergency loans.
However, he stressed that Athens had to be propped up, because if it fell, it would lead "with great certainty to a spillover to other countries," sparking "a type of meltdown," he added.
Ackermann's comments are all the more surprising because they follow recent reports that Deutsche Bank itself was preparing to provide €500 million in loans to Greece on the same conditions as those set by the federal government.
The Financial Times Deutschland reported that Finance Minister Wolfgang Schäuble was trying to persuade Deutsche Bank, along with insurers Allianz and Munich Re, to lend €1 billion in total to Greece as a signal that they had confidence in the country, in a bid to stablise turbulent financial markets.
The European Union and the International Monetary Fund have cobbled together a rescue package for Greece worth some €110 billion in loans over three years, of which Germany is expected to make available €22.4 billion.
The bloc has also pulled together a fund worth almost $1 trillion designed to prevent such crises happening in the future.
The FTD said that Ackermann should have kept his views to himself on this occasion.
"There are some times when it is just better not to say anything," the paper wrote.
Politicians, central bankers and the big players in the world of finance have gone out of their way not to say anything that risked "enflaming the debate" about a possible restructuring of Greece's debt, the paper said.
Now, "Ackermann has broken the taboo."