The issue would be "at least €9.8 billion," the bank said in a statement.
Industry sources told AFP it was the biggest rights issue ever for Deutsche Bank, and the second biggest in German history.
"Through this capital increase, Deutsche Bank intends to secure the equity capital required for a planned consolidation of Postbank," Deutsche Bank chief executive Josef Ackermann said in a statement.
"As a result, we can expand our strong position in our home market, take a leading position in the European retail banking business and significantly enhance Deutsche Bank's revenue mix," he added. "Furthermore, with this capital increase we are strengthening the bank's equity capital in light of expected regulatory changes."
Deutsche Bank currently owns almost one third of the equity in Postbank, which has Germany's largest retail banking network.
The statement said Deutsche Bank would offer Postbank shareholders a price of between €24 and €25 per share for their holdings.
The final minimum price would be set in about one week by Germany's Federal Supervisory Authority BaFin, the firm said.
The news that Germany's biggest bank was seeking to bolster its capital came as leading central bankers and financial regulators met in Basel to hammer out a new framework aimed at preventing a repeat of the global financial crisis.
Banks could have to significantly increase capital reserves that underpin lending to the wider economy, and possibly add an additional buffer, which some bankers warn could curb the amount of credit available to fuel an uncertain recovery.
According to media reports, Deutsche Bank wants to tap capital markets before other banks do to bolster their equity positions in response to the so-called Basel III requirements.
The size of the offering suggests its main aim is to reinforce capital at Deutsche Bank and help the financial giant pull ahead of its weaker German rivals, the Financial Times said on Friday.
Bankers in France and Germany have estimated the new rules may require them to raise some €255 billion, and banks could find themselves in competition with governments if everyone tries to tap capital markets at the same time.
Rumours of the move on Friday sent its shares sharply lower in Frankfurt as traders worried about what it meant for the firm's capital reserves and the effect of the rights issues on existing shareholdings. Shares in Postbank went the other way.
Deutsche Bank said it would hold a news conference and analyst call on the announcement at 9:30 am on Monday (0730 GMT).