The possible deal, which would require the approval of the Federal Reserve and banking regulators in New York, would be the largest takeover of a U.S. bank by a non-U.S. bank, the Financial Times said in Tuesday's edition.
Bankers Trust, based in New York, is the eighth-largest bank holding company in the United States in terms of assets.
The newspaper said sources close to the talks, whom they do not name, stress the discussion is in its early stages, but that it is the "key element" of the German bank's efforts to acquire a leading U.S. investment bank.
Any announcement of any deal is seen as being some way off.
"I would not call these official talks, more exploratory talks," the Financial Times quoted an unidentified person involved as saying. "However, it looks like it may lead to that." The newspaper said both companies declined to comment on the report.
Senior executives at Deutsche Bank are said by Wall Street sources to recognize talks with Bankers Trust as offering the best hope of a takeover announcement before the end of the year, the newspaper said.
Bankers Trust would provide the German bank with a large-scale U.S. operation and U.S. clients.