Germany's largest bank received a subpoena from Mueller several weeks ago to provide information on certain money and credit transactions, the person said, without giving details, adding key documents had been handed over in the meantime.
"Deutsche Bank always cooperates with investigating authorities in all countries", the lender said in a statement to Bloomberg on Tuesday.
Trump got a $106 million loan from Deutsche Bank in 2011 to buy Doral, the golf resort in Miami, according to property filings with the local land register.
The bank has rejected the efforts of House Democrats to provide details of Trump and his family's finances, saying it would be illegal to share client data without a formal request. Trump has denied any wrongdoing.
Mueller is investigating alleged Russian attempts to influence the 2016 US presidential election and potential collusion by Trump aides.
The White House has not yet commented on Mueller's subpoena of Deutsche Bank.
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Specifically, with regards to Hunter's claims, he added, "I still don't know who this woman is". The hour-long session ended shortly after, as the two were unable to move past the issue.
In June, President Trump disclosed that he owes the bank roughly $130 million.
Trump has done billions of dollars' worth of business with Deutsche Bank in the past 20 years; he has previously said that he would consider Mueller looking into his finances beyond any connection to the Russian Federation investigation "a violation". The lion's share, a $170-million loan, relates to the luxury hotel the Trump Organization opened in Washington, D.C. inside the refurbished Old Post Office building.
Mr. Mueller's investigation has led to charges against former Trump campaign chairman Paul Manafort and his longtime business partner Rick Gates for work unrelated to the campaign.
Federal Bureau of Investigation (FBI) Director Robert Mueller testifies during a hearing before the Senate Judiciary Committee June 19, 2013 on Capitol Hill in Washington, DC.
Mueller has also obtained a guilty plea from Trump campaign foreign policy advisor George Papadopoulos.