Speaking to German television channel NTV on the sidelines of the World Economic Forum in Davos, Josef Ackermann said: "I am confident that a solution can be found."
He said the "haircut", or losses that banks were being asked to take on their holdings of Greek debt, was "almost 70 percent."
"That is a great, great deal. But everyone has to make their contribution and then we will see where we are. We're going to carry on," said Ackermann.
Negotiations between Athens and private creditors -- including Deutsche Bank -- aim to reach agreement on a voluntary exchange of bonds that would wipe €100 billion ($130 billion) off the country's debt of €350 billion.
The Private Sector Involvement (PSI) deal, agreed in principle in October, foresees creditors taking a "haircut" of at least 50 percent on the €200 billion in debt they hold. Deutsche Bank held around €900 million of Greek debt as of September 30.
Two previous rounds of talks have snagged on the amount of interest to be
paid on the new bonds following the exchange.
Adding to the growing sense of optimism, EU Economic and Monetary Affairs Commissioner Olli Rehn said he expected a deal to be clinched soon.
Speaking in Davos, he said: "They're about to close a deal, if not today maybe over the weekend, preferably in January rather than February."
And Steffen Seibert, spokesman for German Chancellor Angela Merkel, also added that Berlin was "confident" that the talks would conclude soon.