The German business newspaper Handelsblatt, which first reported the subpoena, quoted a spokesman saying that the bank cooperates with official investigators but would not discuss individual cases.
Trump has also said that it would be a "violation" if Mueller went into his family's finances instead of focusing directly on the mechanisms of influencing the election, part of suggestions that he could fire the former Federal Bureau of Investigation director.
Deutsche Bank did not immediately respond to a request for comment. Russian Federation has denied meddling in the election and Trump has called the special counsel's investigation a "witch hunt".
In a July 9 interview with the New York Times, Trump said Mueller should not extend his investigation into Trump's finances if they were not directly related to the Russian Federation accusations. I don't have buildings in Russian Federation. This means Trump is overseeing a government that has had to make tough decisions over how to handle various matters related to Deutsche Bank-to which he owns a ton of money. I don't. It's not my thing. But Cohen said those talks never yielded anything.
Deutsche Bank management is ready to share information about the lender's dealings with Trump and is hopeful that doing so will help end the series of inquiries from Democrats, an executive at the bank, who asked not to be identified discussing private deliberations, has previously told Bloomberg News.
White House lawyers declined to comment on Mueller's expenditures.
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Trump's super-sized Deutsche Bank loans-as well as his debts to other lenders-create massive conflicts of interest.
According to media reports, Mr. Trump owed Deutsche Bank as much as $340 million (€286.5 million) at one point, though considerable restructuring appears to have brought down that amount. He cites "Schiff" for that tidbit, who presumably is Democratic Congressman Adam Schiff, a ranking member of the committee.
Mr Trump and Deutsche Bank have not always been on good terms. Mueller's law enforcement powers may mean he gets a different result. More recently, though, he has highlighted news reports that Peter Strzok, the former top FBI official assigned to the investigation, was reassigned after it was discovered he and another team member had exchanged texts disparaging Trump and supporting Clinton.
Mr Trump has repeatedly denied any collusion with Russian Federation, calling the allegations a "witch hunt". And he also has deep financial entanglements with alleged Russian oligarchs and mobsters. By the way, I would say, I don't - I don't - I mean, it's possible there's a condo or something, so, you know, I sell a lot of condo units, and somebody from Russian Federation buys a condo, who knows?
One key indictment has been of former Trump campaign chairman Paul Manafort, who was accused of laundering $75 million in relation to work he did for the former Moscow- backed Ukrainian leader Viktor Yanukovych. Mueller's prosecutors say they hid millions of dollars in payments from overseas.