The German bank is said to have approved huge loans to Mr Trump even after bankruptcies and defaults led to him being “deemed untouchable” by most financial institutions.
The report comes as congressional committees and New York’s attorney general investigate Mr Trump’s links to Deutsche Bank.
Mr Trump’s relationship with company began in the late 1990s and lasted until his presidential campaign in 2016, according to the Times, which interviewed more than 20 current or former Deutsche Bank executives and board members.
Their ties developed as the bank was reportedly attempting to make inroads in Wall Street by taking on high-risk investments.
According to the report, Mr Trump wooed Deutsche Bank investors on his private jet and promised them trips to his Mar-a-Lago resort in Florida in a bid to secure deals.
Seeking to obtain a $500m (£377m) loan to build a 72-storey skyscraper in Chicago, Mr Trump is said to have told the bank his net worth was $3bn (£2.3bn). When Deutsche Bank employees reviewed his finances, they concluded his wealth was actually $788m (£594m).
The company still made the loan in 2005, but Mr Trump struggled to sell hundreds of apartments in the resulting Trump Tower. With the bulk of the loan repayment due in November 2008, his lawyers claimed the financial crisis was an act of God that meant he was not liable. The bank and Mr Trump sued each other, but the dispute was later settled out of court.
In 2010, Mr Trump again reportedly exaggerated his wealth as he sought a loan to fund his purchase of a $100m (£75m) golf resort. The bank determined he had overvalued some of his assets by up to 70 per cent, but nonetheless signed off the loan.
Deutsche Bank sought to limit scrutiny of its relationship with Mr Trump after he was sworn in as president, telling employees not use the word “Trump” in external communications, according to the Times.
The bank’s managers were said to be concerned Mr Trump could default on his loans, forcing the company to choose between seizing his assets and cutting him a lucrative break.
The House of Representatives financial services and intelligence committees have each launched probes into Mr Trump’s ties with Deutsche Bank since Democrats took control of the chamber.
The New York State attorney general’s office also issued subpoenas to the bank last week for financial records relating to the Trump Organisation.
A Deutsche Bank spokeswoman said the company was “committed to cooperating with authorised investigations”.