Der Spiegel, citing unnamed sources, said the shareholders had "concrete thoughts" about replacing him. Der Spiegel didn't name the investors it said were pressing for the change.

Achleitner, under pressure from shareholders for some time, survived a confidence vote at May's annual shareholders' meeting. But Deutsche shares hit a record low on Friday, highlighting investor scepticism about the bank's latest turnaround plan.

Achleitner has begun the search for a successor but intends to complete his term, people familiar with the matter have told Reuters.

Der Spiegel named Bundesbank President Jens Weidmann and Munich Re Chairman Nikolaus von Bomhard as two people who fit the profile for a possible successor, but it added that neither had been approached.

Deutsche Bank said in a statement: "Mr. Achleitner is mandated until 2022. Furthermore, all questions regarding succession planning on the supervisory board are handled by the nomination committee."

The office of von Bomhard didn't immediately respond to a request for comment.

The Bundesbank declined to comment. Munich Re didn't respond to a request for comment.

Deutsche Bank shares fell as low as 5.777 euros (5.3 pounds), below their previous record low of 5.8010 euros set on June 3, before closing up 4.7% at 6.16 euros.

(Reporting by Hans Seidenstuecker, Patricia Uhlig and Tom Sims; Editing by David Holmes)