"Trump lawyer John Dowd said the information was passed to Trump by White House counsel Donald McGahn, who had been warned about Flynn's statement to the vice president by a senior Justice Department official".
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.
Although limited in detail, the spending report offers the first insight into the scope and scale of Mueller's investigation, which has resulted so far in criminal charges against four people who worked on Trump's presidential campaign.
Mr Trump has repeatedly denied any financial connections with Russian Federation.
An internal investigation carried out by Deutsche Bank didn't yield any evidence of connections between the client relationship with Trump and the bank's mirror trades affair, a person briefed on the matter said.
During his election campaign, Mr Trump said he would seek to improve ties with Russian President Vladimir Putin, which were strained during former president Barack Obama's administration. It was the first time Mr. Trump had said anything other than Mr. Flynn was sacked for lying to Mr. Pence.
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. Trump's former national security adviser, Michael Flynn, pleaded guilty Friday to lying to Federal Bureau of Investigation agents, becoming the fourth associate of the president ensnared by Mueller's probe.
In January, Deutsche Bank agreed to pay US$630 million in fines for organising US$10 billion in sham trades that could have been used to launder money out of Russian Federation.
The Trump International Hotel is shown on August 10, 2017 in Washington.
The German bank is one of the few major lenders that have lent large amounts to Mr Trump in the past decade. "Then Justice claimed that providing House investigators with classified material could hurt security or sources". Over the weekend on Twitter, he attacked the Federal Bureau of Investigation and Mueller's team and defended some of Flynn's actions.
However, White House spokeswoman Sarah Sanders rejected reports of a subpoena for Trump-related financial records as "completely false", as did Trump's personal attorney Jay Sekulow.