The Reuters news agency had reported that Deutsche Bank received a subpoena from Mr Mueller several weeks ago, citing a person close to the matter.
It said investigators wanted information on certain money and credit transactions, and that key documents had already been handed over.
But in a statement, the President’s lawyer Jay Sekulow said: “We have confirmed that the news reports that the Special Counsel had subpoenaed financial records relating to the President are false. No subpoena has been issued or received. We have confirmed this with the bank and other sources.”
Mr Mueller is looking into claims of Russian interference in the US presidential election and potential collusion by Mr Trump’s team – an allegation denied by the President and Russian authorities.
Deutsche Bank, the largest bank in Germany, has lent the Trump organisation hundreds of millions of dollars for real estate deals.
Bankruptcies at his hotel and casino business in the 1990s made much of Wall Street shy away from lending Mr Trump credit, forcing him to look further afield.
In June, the German bank rejected a demand by Democrats to provide details of the President’s finances, citing privacy laws.
But some details are in the public domain: Mr Trump received a $106m loan from Deutsche Bank in 2011 to buy the Doral golf resort in Miami, according to the local land register.
In 2012, his Trump International Hotel Hotel and Tower in Chicago was loaned up to $640m, according to a property filing.
The German bank also lent him $170m to turn the Old Post Office in Washington into a luxury hotel, which opened last year.
US Democrats have argued federal laws protecting customer confidentiality do not apply to requests from US Congress.
Deutsche Bank agreed in January to pay $630m in fines for organising $10bn in sham trades that could have been used to launder Russian money.
Reports of the subpoena came after Mr Trump’s former national security adviser, Michael Flynn, last week admitted he had lied to the FBI over his contact with Russia’s ambassador and agreed to cooperate with Mr Mueller’s investigation.
It also prompted claims among Trump opponents that the President may have obstructed justice, after a tweet at the weekend appeared to confirm he knew at the time of Mr Flynn’s sacking that he had lied.
The President denies he attempted to pressure ex-FBI director James Comey “to let Flynn go” and has savaged the bureau, saying its reputation is in “tatters”.