Citing sources close to the matter, it said Allianz would eventually like to merge Postbank, controlled by the logistics group Deutsche Post, with its own commercial bank, Dresdner Bank.
It said Deutsche Post wants to sell Postbank, which has attracted considerable interest because of its strong position in German retail banking. An Allianz spokesman contacted by AFP declined comment. Postbank, Commerzbank and Deutsche Post were all unavailable as Thursday is a religious holiday in much of Germany.
Postbank shares rose 2.19 percent to €61.20 on news of the report on the Frankfurt exchange, which was generally stronger.
The possible sale of Postbank has sparked comment in Germany where it could signal a decisive move toward consolidation in the banking sector and could see the birth of a German financial "national champion."
The fate of Postbank has been followed closely by the German government, a major shareholder in Deutsche Post.