Bankers said a deal would give the combined operation the balance sheet strength to underwrite the big corporate deals and weather the tough market conditions many fear are in store for the industry.
However, they cautioned that while both banks have respectable fixed- income businesses, putting the equity businesses together would still leave the group well behind the leading Wall Street houses.
Neither bank would comment. Banking sources said they were sure there had been contacts between the two institutions, but these were "very, very preliminary" and there were doubts about whether they would lead to a takeover of the US bank.
Deutsche Bank's chief executive, Rolf Breuer, said in a press interview that the bank, Germany's largest, was still keen to make a big US purchase despite stock market turmoil.
Bankers Trust, which reports third-quarter earnings tomorrow, has been buffeted in the past few days by rumours about its financial health.
Deutsche, which bought City merchant bank Morgan Grenfell in 1989 and has made several attempts to create its own global-scale investment bank, is believed to have approached a string of US securities houses including JP Morgan, Hambrecht & Quist and Lehman Brothers.
John Leonard, banks analyst at Salomon Smith Barney, said it was hard to see a merger succeeding given the cultural problems of integrating a German and US bank.
Other banks also saw sharp share price gains yesterday as investors took the reports that Deutsche and BT were talking as a signal that recent worries about banking exposures were overdone and that prospects for consolidation were improving.