Deutsche Bank has complied with the subpoena and provided the Manhattan District Attorney's office with Trump's financial records, including materials he submitted to the bank for loans, the New York Times report said on Wednesday.
The report said the inquiry indicates the investigation is more wide-ranging than previously known.
In a court filing this week, the report said, prosecutors suggested that they were also investigating possible crimes of bank and insurance fraud.
The investigation and inquiry into Deutsche Bank are still at an early stage, the report said, citing a person briefed on the matter.