Investigators -- who are probing whether Trump's campaign colluded with Moscow to swing last year's US presidential election -- presented Germany's biggest bank with a demand for information about Trump and members of his family, Bloomberg News and German business daily Handelsblatt reported, citing anonymous sources.
The subpoena arrived "a few weeks ago," according to the German paper, which added that the most important files relevant to the request have already been sent to Mueller's team.
Investigators were looking for "information about specific financial and credit transactions with the Trump family," Handelsblatt reported.
An internal investigation at Deutsche "found no suspicious connections between Trump and Russia so far," Handelsblatt added.
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Trump has a history of dealings with Deutsche Bank during his career as a New York property mogul, and his businesses owed it around $300 million in July 2016 according to a Bloomberg analysis.
Meanwhile, the president's wife Melania, his daughter Ivanka and her husband Jared Kushner are all customers of Deutsche's wealth management arm, according to Handelsblatt.
In a separate case, Deutsche was fined almost $630 million by US and British authorities over money laundering earlier this year, after moving USD 10 billion illegally out of Russia using a so-called "mirror trading" scheme.
The Republican leader's opponents in the US have called on Deutsche to provide more information on the relationship.
But the bank has so far refused to meet the demands, saying releasing any data would be illegal.
Mueller's probe into Trump has intensified in recent months, with a flurry of charges in late October against former Trump campaign director Paul Manafort, his deputy Richard Gates and campaign official George Papadopoulos.
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