Banking regulators have spent months investigating Jeffrey Epstein’s dealings with Deutsche Bank, which lent money to the disgraced financier and held dozens of accounts for him until shortly before he died, according to four people briefed on the matter but not authorized to speak publicly.

The investigation by the New York Department of Financial Services, which has not been previously reported, could result in an enforcement action against Deutsche Bank as soon as this month, before the first anniversary of Mr. Epstein’s arrest on federal sex-trafficking charges, the people said. Mr. Epstein was arrested on July 6 and died in federal custody in August; his death was ruled a suicide.

The investigation focuses, at least in part, on the bank’s decision to continue doing business with Mr. Epstein even after employees raised concerns, according to the people. Compliance officers in the bank’s anti-money-laundering operation alerted the federal government to several transactions in which Mr. Epstein sent money overseas in 2015, while employees worried about the reputational risks of doing business with a registered sex offender. Ultimately, senior bank executives opted to maintain the relationship with Mr. Epstein because it was so lucrative.

In addition to setting up dozens of accounts for Mr. Epstein, Deutsche Bank served as his lender from 2013 until last year, even as other banks considered him off-limits. Deutsche Bank began extricating itself from its relationship with Mr. Epstein in late 2018, after a series of articles in The Miami Herald examined the secret nonprosecution agreement federal prosecutors reached with him in 2007. Deutsche Bank told Mr. Epstein he had six months to move his money out of the bank.

Daniel Hunter, a Deutsche Bank spokesman, said the bank regarded its reputation as its “most precious asset.”

“We regret the decision to associate with Epstein,” he said.

After Mr. Epstein was arrested last July, Deutsche Bank executives began an internal investigation into the bank’s relationship with him. The examination includes studying how Mr. Epstein used his accounts and the bank’s decision to keep him as a client, even as other banks had distanced themselves from him.

Bank officials have been sharing their findings with New York regulators, according to the people briefed on the matter. The Department of Financial Services wields significant power over Deutsche Bank because the agency licenses it to operate in the state, where the bank has most of its U.S. operations.

If state regulators decide to punish Deutsche Bank, it would be the latest in a series of black eyes for the bank. Federal and state authorities in recent years have imposed billions of dollars of fines on the German bank for failing to stop money laundering and for violating sanctions, among other things. The bank also has been under scrutiny by congressional Democrats and state prosecutors for its role as the longtime banker to President Trump, his family and his companies.

An enforcement action against Deutsche Bank would be the first taken by regulators against any of the banks that Mr. Epstein used to handle his money as he built a fortune of more than $600 million, according to court filings by his estate. But other financial institutions and bankers are also being scrutinized by government officials in the United States and abroad.

‘Another Customer Was Appalled to Witness Such Blatant Favoritism’

The attorney general for the United States Virgin Islands, Denise George, subpoenaed years of records from First Bank, a Puerto Rico-based lender that had provided banking services to Mr. Epstein for nearly two decades, according two people briefed on that investigation but not authorized to speak publicly. In January, Ms. George’s office filed a civil forfeiture lawsuit against Mr. Epstein’s estate, in which she contends that Mr. Epstein misled government officials there for nearly two decades and used a private island hideaway to engage in sex trafficking.

Ms. George is also looking into millions of dollars of transactions conducted last year — both before and after Mr. Epstein’s death — at a little-known bank that he had established in the Virgin Islands called Southern Country International.

And bank regulators in Britain are looking into whether James E. Staley was transparent about the details of his relationship with Mr. Epstein when describing it to officials at Barclays, where Mr. Staley became chief executive in 2015. Barclays has stood behind Mr. Staley, who has said he had no contact with Mr. Epstein after 2015.

Before joining Barclays, Mr. Staley was a senior executive at JPMorgan Chase, where he helped cultivate that bank’s relationship with Mr. Epstein.

JPMorgan was Mr. Epstein’s primary bank for more than a decade, but some bank officials became uneasy about doing business with him after his 2008 guilty plea to soliciting prostitution from a minor in Florida. JPMorgan cut ties with Mr. Epstein after Mr. Staley left the bank in 2013.

That is when Mr. Epstein began working with Deutsche Bank. Paul Morris, a private banker who had recently arrived at the German bank from JPMorgan, brought Mr. Epstein on as a client, according to two of the people briefed on the matter. Mr. Morris, who left Deutsche Bank for another firm in 2016, did not respond to requests for comment.

The investigation could provide a rare glimpse into Mr. Epstein’s mysterious finances.

Mr. Epstein made a significant portion of his fortune while banking with Deutsche Bank, even though his criminal record had cost him his most lucrative client, Leslie Wexner, the billionaire retail magnate who built Victoria’s Secret into a household name. Mr. Wexner gave Mr. Epstein a sweeping power of attorney to manage all aspects of his financial affairs, but said he severed all ties with Mr. Epstein shortly before his guilty plea.

While Mr. Epstein was a client of Deutsche Bank, his main business was Southern Trust Company, which generated more than $250 million in revenues during its existence, according to public records. Mr. Epstein created the company in 2013 and told government officials in the Virgin Islands that it was involved in DNA analysis and research.

Ms. George, in her civil forfeiture lawsuit, contends that Southern Trust was not in the business it claimed to be and that Mr. Epstein misled government officials in order to win a lucrative tax break. She told The New York Times in March that her office had not yet determined the kind of business Southern Trust was in.