Speculation has arisen that the company may split the job between the head of the investment bank and the chief of operations in Germany.

Some have suggested that Anshu Jain, an Indian-born executive who oversees the bank’s trading and transaction businesses, could share chief executive duties with Jürgen Fitschen, a member of the bank’s management board whose responsibilities include Deutsche Bank’s German operations.

The businesses overseen by Mr. Jain, 48, generate far more profit than the bank’s other units combined. But he is not fluent in German and is seen as ill-suited to handle the political and ceremonial responsibilities that are expected of the head of the country’s signature bank.

Mr. Ackermann, whose contract as chief executive runs until 2013, was a crucial adviser to Chancellor Angela Merkel during the global financial crisis.

He has also been a spokesman for the banking industry on regulation, serving as chairman of the Institute of International Finance, an association of the world’s biggest banks, including Goldman Sachs, Morgan Stanley and Citigroup.

At the same time, Deutsche Bank risks losing Mr. Jain, its top moneymaker and a favorite of investors, if he does not get the top job. Mr. Jain and Mr. Fitschen, who oversees Deutsche’s regional operations worldwide, have a very good relationship, say people who know both men.

Mr. Fitschen, 62, could oversee the bank’s efforts to reduce its dependency on volatile and risky investment banking, and expand its more stable businesses like corporate lending and retail banking. Then, the thinking goes, Mr. Fitschen could retire in a few years, clearing the way for Mr. Jain to serve as sole chief executive once he had the chance to learn more about other areas of the bank.

In recent months, the German news media have reported on supposed friction between Mr. Ackermann and Clemens Börsig, the current chairman of the supervisory board. Also, there are signs that the succession debate is straining relations between Mr. Ackermann and Mr. Jain.

“The public back-and-forth over personnel has increasingly damaged the image of the bank,” the Frankfurter Allgemeine Zeitung said Sunday in an editorial.

There has been more pressure to decide on a successor to Mr. Ackermann after Axel Weber, former head of the Bundesbank, took a job at UBS, Deutsche Bank’s Swiss rival. Mr. Ackermann had advocated pairing Mr. Weber with Mr. Jain to address his concern that Mr. Jain was not ready to assume the more ceremonial aspects of the job.

A nominating committee of the bank’s supervisory board was expected to meet late Sunday to discuss succession. But the bank said on Sunday afternoon that it would not have any statement after the meeting, though the succession issue has unsettled investors and hurt the institution’s image.

The bank denied a report by Der Spiegel, the German news magazine, that Mr. Ackermann was seeking to become chairman of the bank’s supervisory board, a part-time oversight position.

Mr. Ackermann, who has led the bank since 2002, has said on numerous occasions that he did not want to take over the supervisory board when he retired as chief executive. Such a move is common practice among retiring chief executives in Germany, but is regarded also as poor corporate governance. The new chief may not be able to make necessary changes if his predecessor continues to loom over him.

“His position on switching to the supervisory board has not changed,” Deutsche Bank said of Mr. Ackermann in a statement.

Jack Ewing reported from Frankfurt and Landon Thomas Jr. from London.

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