The banking giant's supervisory board could meet as soon as Sunday to decide on the "tough cuts" set to hit the business, daily Frankfurter Allgemeine Zeitung reported Monday without naming a source.
The cuts are part of the lender's restructuring programme. Chief executive Christian Sewing dangled the prospect of layoffs at Deutsche's annual general meeting in May.
Several media reported that up to 20,000 jobs could be on the chopping block, out of the total 91,500 staff.
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However, the decision hasn’t been formally adopted yet and the number may yet change, they said.
Top of the list for cuts is the investment bank. Once the flagship division of the group, the 37,000-strong unit has been undermined by scandal for years.
Shares in Germany's biggest lender rose Monday, as investors reacted to the multiple press reports detailing how the financial firm plans thousands of layoffs in its battle to escape a years-long malaise.
By 1:15 pm in Frankfurt, Deutsche stock had added 1.6 percent at €6.89, against a DAX index of blue-chip German shares up 1.2 percent.
Deutsche is doing "better than other European banks on Monday," said MM Warburg analyst Andreas Plaesier, drawing a connection to the hints about its future that have trickled out in recent days.
Staff let go
Last year, one-quarter of its stocks trading staff in the US were let go, and a source close to the bank told AFP more such steps could be coming.
Sharp reductions in the payroll were feared earlier this year when Deutsche entered detailed talks on a potential merger with hometown rival Commerzbank but the deal fell through in April.
At the top of the bank, a board reshuffle could also be on the cards according to press reports, with investment banking chief Garth Ritchie reportedly slated to leave.
Away from staffing questions, as Deutsche looks to tidy up its balance sheet it could dispose of up to 50 billion euros of loans and other assets seen as non-strategic, the Financial Times reported recently.
Deutsche shares had already benefited last Friday from its American division's success in banking stress tests by the US Federal Reserve, a result hailed by Sewing in a letter to employees.
Looking ahead, the firm will unveil its second-quarter results on July 24th.