But the bank, Germany's largest private financial institution, said it was merely pressing ahead with restructuring already underway.
"We won't comment on the figures. But we announced last October a plan to cut 1,100 jobs in Europe and at the same time the creation of 2,500 client advisory posts. That has not changed," a bank spokesman said.
However, Die Welt reported that Deutsche Bank wanted to eliminate or farm out 1,300 German jobs, but without resorting to outright redundancy.
In late 2008, Deutsche Bank employed 80,000 people worldwide, including almost 28,000 in Germany. It warned in March that some jobs might be cut.
But the bank appears to have rebounded from the international financial crisis after suffering a hit last year. In both the first and second quarters of this year it has posted net profit of more than €1 billion ($1.46 billion).