Authorities around the world are examining whether traders from different banks worked together to influence currency prices, and also whether they traded ahead of their own customers or failed to accurately represent to customers how they were determining the prices.
"So far we have only found isolated cases but they are anything but reassuring. These are possibly criminal acts that could happen because checks failed," Raimund Roeseler told the Wirtschaftswoche weekly in an advance copy ahead of publication.
He said the investigation would still take some time, adding it was an enormous market.
Earlier this month, U.S., British and Swiss regulators fined six major banks a total of $4.3 billion for failing to stop traders from trying to manipulate the foreign exchange market, following a year-long global investigation.
Roeseler declined to confirm that a separate investigation into Deutsche Bank over possible efforts to manipulate benchmark interest rates would be concluded this year.
Deutsche Bank has said it was cooperating with regulators and industry sources have said the bank is hoping to settle the affair with regulators before the New Year.
(Reporting by Emma Thomasson; Editing by Clelia Oziel)