According to a report in Sunday's Bild am Sonntag newspaper, DM6.41 billion in notes and DM6.9 billion in coins were never converted after the euro was introduced on January 1, 2002. Altogether, they would be worth €6.8 billion.
The cash, which works out at DM162 per German, is thought to have been stashed away and long forgotten, or else left abroad by holidaymakers and immigrants.
The Deutsche Mark was also often used as currency in the Balkan region during the wars of the 1990s, and much of the missing cash is thought to be still hidden away, even buried, in the former Yugoslavia.
On top of this, wads of old banknotes are still occasionally discovered when deceased people's homes are cleared out.
A German Federal Bank spokesman told the paper that the bank expects that a large part of the money will never be converted into euros.
Forty-seven branches of the federal bank still exchange old DM banknotes into euros at no charge, though statistics show that less is exchanged every year. In 2011, only DM140 million was converted, compared to DM180 million in 2010.
The banks says it will even exchange damaged notes, as long as the metal strip is still in place, or more than half of the note is still left.
According to Deutsche Bank, the missing €6.8 billion would theoretically give the German economy an extra boost of 0.27 percent if it were brought back into circulation.