By Donald Trump’s reckoning, his relationship with Wall Street could not be better.

“I am friends with all the major banks,” he said in an interview. “They are dying to do business with me.”

The presumptive Republican nominee recently tapped Steven T. Mnuchin, a former Goldman Sachs partner and chairman and chief executive of Dune Capital Management, a private investment firm, as his national finance chairman. Carl C. Icahn, the billionaire activist shareholder, was an early supporter. Thomas J. Barrack Jr., founder and executive chairman of the private equity firm Colony Capital, is scheduled to host a Los Angeles fund-raiser later this month, Mr. Mnuchin said.

“I think we will have very broad support,” Mr. Mnuchin said of the financial community.

Still, an examination of financial records and interviews with nearly two dozen executives at financial firms show that Mr. Trump’s relationship with the financial industry is far more nuanced than he suggests.

While some bankers said they had a personal relationship with Mr. Trump, a majority of those interviewed about him said they had never met him, and either had not done business with him or would not do so because of past dealings that did not end well.