Mr Mueller is investigating claims of collusion between Trump's aides and Russian officials while also probing Moscow's influence in the United States presidential election which brought Trump, the billionaire businessman into power.
In a statement Tuesday, attorney Jay Sekulow says such reporting is "false" and says "no subpoena has been issued or received".
The heat on the investigation of President Trump's finances has just been cranked up even further.
Statues stand outside a Deutsche Bank AG bank branch in Frankfurt, Germany, on October 20, 2016.
Mr Mueller issued a subpoena to the bank several weeks ago demanding data on transactions linked to the U.S. president, Reuters news agency and a German newspaper say.
Asked if delving into his and his family's finances unrelated to the Russian Federation probe would cross a red line, Trump replied, "I would say yeah". After a string of bankruptcies and broken promises, pretty much every other major bank stopped lending Trump money some years ago. "Over the years, I've looked at maybe doing a deal in Russian Federation, but I never did one". He had reached a tentative agreement with the government.
"Deutsche Bank's pattern of involvement in money laundering schemes with primarily Russian participation, its unconventional relationship with the president, and its repeated violations of USA banking laws all raise serious question about whether the bank's reported reviews of the trading scheme and Trump's financial ties to Russia were completely thorough", they wrote.
There was no immediate response to the Deutsche Bank subpoena from Trump's lawyers.
Deutsche Bank is not the only Trump-related business interest that is attracting the attention of investigators. 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.
In June, Deutsche Bank already rejected demands by US House Democrats to provide details of Trump's finances, saying sharing client data would be illegal unless it received a formal request to do so. And he also has deep financial entanglements with alleged Russian oligarchs and mobsters.
A day later, the DOJ announced that former Trump campaign aide George Papadopoulos pleaded guilty to lying to federal agents during the investigation about his contacts with three individuals said to have had connections to the Russian government.
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