Josef Ackermann made the comments when questioned for an appearance on German television ZDFâs website.
The chief of the financial institution said that the ailing nation needed a sizeable bailout package as, if it were to collapse, it may trigger some form of âmeltdownâ across other financial markets within Europe.
However, Mr Ackermann told the news provider: "I would doubt that Greece over time will be in a position to come up with the economic potential to pay back the bailout money."
A bailout package of â¬750 billion for Greece was agreed earlier in the week by states within the eurozone.
The European Central Bank has also agreed on a $1 trillion bailout package, which the Deutsche Bank CEO said should enable Spain and Italy to survive the financial difficulties they are experiencing.
Mr Ackermann said that the two states were âstrong enoughâ to get through the crisis following the announcement, although it may be more âdifficultâ for Portugal to follow suit.
According to reports, Greece is the first country for 11 years to require a political pledge of support because of its debt issues.
By Jim Ottewill