He confirmed the bank in question was Deutsche Bank.
In June Deutsche Bank cited privacy laws when it rejected a request by House Democrats to provide details of Trump's finances.
Mueller is investigating alleged Russian attempts to influence the 2016 United States presidential election and potential collusion by Trump aides.
In May, five Democratic members of the House of Representatives sent a letter to Deutsche Bank CEO John Cryan asking the bank to turn in any records relating to Trump's accounts and any ties to Russian Federation. The bank said additionally in a statement that "Deutsche Bank takes its legal obligations seriously and remains committed to cooperating with authorized investigation into this matter".
On Monday, as he left the White House for a trip to Utah, Trump restated his sympathy for Flynn and his assertion that prosecutors should have pursued action against his general election rival, Hillary Clinton. The Mueller investigation now wants the bank to detail any ties between those trades or other Russian financing as it seeks to identify anyone connected to Donald Trump, his family or advisers.More news: YouTube CEO Talks about Increasing Regulatory Staff
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"I think that's a violation", Mr. Trump told the paper.
"No-one from the VTB Group representatives has received a subpoena because there are absolutely no grounds for it", a bank representative said in response to a request from Reuters.
Trump's relationship with Deutsche Bank stretches back some two decades and the roughly $300 million he owes to the bank represents almost half of his outstanding debt, according to a July 2016 analysis compiled by Bloomberg news agency.
Mr Trump and Deutsche Bank have not always been on good terms.
Deutsche Bank has also come under scrutiny for activities in the same world it shares with Trump, real estate investment. Mueller's investigation had expanded to examine a broad range of transactions involving the president's businesses, including dealings by his son-in-law, Jared Kushner, and Commerce Secretary Wilbur Ross, a person familiar with the probe told Bloomberg News after the publication of the Times interview.