The president has said that inquiries into his financial dealings would be a "violation" of the special counsel's mandate. Mueller is investigating ties between the president's top advisers and Russia.
Trump has repeatedly denied accusations that his campaign colluded with the Russian government.
Press secretary Sarah Sanders on Tuesday called the reports that Mueller subpoenaed Deutsche Bank "totally false."
"I think this is another example of the media going too far too fast," she told reporters at a press briefing.
Sol Wisenberg, a leading white-collar attorney who was deputy independent counsel in the Whitewater investigation, said it's typical for the subject of a subpoena to be informed that prosecutors sought his records.
But, he said, a financial institution cannot inform its client or anyone named in the subpoena if the prosecutor requests that the institution not do so.
Earlier on Tuesday a Deutsche Bank spokesperson told NBC, "DB takes its legal obligations seriously and remains committed to cooperating with authorized investigations into this matter."
The lender declined to say what constituted an authorized investigation, and whether the Mueller inquiry was included.