Mr Mueller issued a subpoena to the bank several weeks ago demanding data on transactions linked to the United States president, Reuters news agency and a German newspaper say.
In a statement Tuesday, attorney Jay Sekulow says such reporting is "false" and says "no subpoena has been issued or received".
"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.
The Trump family's dealings with Deutsche Bank have been a focus of opponents for months. But the fact that Mueller is looking at Deutsche Bank means his probe is reaching the very heart of Trump's financial life.
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CNN Congressional Correspondent Manu Raju tweeted that Republicans on the House Intelligence Committee actually blocked the Trump finances subpoena, refusing to order Deutsche Bank to hand over the Trump Organization's financial records.
Mueller's probe also caused other Justice Department components to spend about $3.5 million on work attributable to the special counsel probe, according to the report. Kushner also flatly denied Russian financial connections when he talked with members of Congress this fall.
While Trump campaigned during the 2016 election, the bank rejected calls to be transparent about exactly how much money Trump owes and why. Mueller's 17 lawyers - some reassigned from within the government and others brought in from private practice - have charged or negotiated plea deals with four former Trump campaign or administration officials, including former campaign chairman Paul Manafort and former Trump national security adviser Michael Flynn.
During his White House campaign, Trump said he would seek to improve ties with Russian President Vladimir Putin, which had been frequently strained during President Barack Obama's administration.
That's a whole lot of people around Trump who are acting like they have something to hide. If Mueller is getting deep into Trump's finances, we may well find out just what he's been working so hard to keep the public from finding out.
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