State prosecutors in Manhattan have interviewed several employees of President Trump’s bank and insurance broker in recent weeks, according to people with knowledge of the matter, significantly escalating an investigation into the president that he is powerless to stop.

The interviews with people who work for the lender, Deutsche Bank, and the insurance brokerage, Aon, are the latest indication that once Mr. Trump leaves office, he still faces the potential threat of criminal charges that would be beyond the reach of federal pardons.

It remains unclear whether the office of the Manhattan district attorney, Cyrus R. Vance Jr., will ultimately bring charges. The prosecutors have been fighting in court for more than a year to obtain Mr. Trump’s personal and corporate tax returns, which they have called central to their investigation. The issue now rests with the Supreme Court.

But lately, Mr. Vance’s office has stepped up its efforts, issuing new subpoenas and questioning witnesses, including some before a grand jury, according to the people with knowledge of the matter, who requested anonymity because of the sensitive nature of the investigation.

The grand jury appears to be serving an investigative function, allowing prosecutors to authenticate documents and pursue other leads, rather than considering any charges.

When Mr. Trump returns to private life in January, he will lose the protection from criminal prosecution that his office has afforded him. While The New York Times has reported that he discussed granting pre-emptive pardons to his eldest children before leaving office — and has claimed that he has the power to pardon himself — that authority applies only to federal crimes, and not to state or local investigations like the one being conducted by Mr. Vance’s office.

Mr. Trump, who has maintained he did nothing improper, has railed against the inquiry, calling it a politically motivated “witch hunt.”

The investigation by Mr. Vance, a Democrat, has focused on Mr. Trump’s conduct as a private business owner and whether he or employees at his family business, the Trump Organization, committed financial crimes. It is the only known criminal inquiry into the president.

Employees of Deutsche Bank and Aon, two corporate giants, could be important witnesses. As two of Mr. Trump’s oldest allies — and some of the only mainstream companies willing to do regular business with him — they might offer investigators a rich vein of information about the Trump Organization.

There is no indication that either company is suspected of wrongdoing.

Because grand jury rules require secrecy, prosecutors have disclosed little about the focus of the inquiry and nothing about what investigative steps they have taken. But earlier this year, they suggested in court papers that they were examining possible insurance, tax and bank-related fraud in the president’s corporate dealings.

In recent weeks, Mr. Vance’s prosecutors questioned two Deutsche Bank employees about the bank’s procedures for making lending decisions, according to a person familiar with the interviews. The employees were experts in the bank’s underwriting process, not bankers who worked with the Trump Organization, the person said.

While the focus of those interviews was not on the relationship with Mr. Trump, bank officials expect Mr. Vance’s office to summon them for additional rounds of more specific questions in the near future, the person said.

Glimpses into the investigation have come in court records during the bitter and protracted legal battle over a subpoena for eight years of Mr. Trump’s personal and corporate tax returns and other financial records.

A month after Mr. Vance’s office demanded the documents from the president’s accounting firm, Mazars USA, in August 2019, Mr. Trump sued to block compliance with the subpoena. The case has twisted its way through the federal courts, with the president losing at every turn, and is now in front of the Supreme Court for the second time.

Danny Frost, a spokesman for Mr. Vance, declined to comment on recent moves in the investigation. Alan Garten, the Trump Organization’s general counsel, declined to comment, but recently said that the company’s practices complied with the law and called the investigation a “fishing expedition.”

Aon confirmed that the company had received a subpoena for documents from the district attorney’s office but declined to comment on the interviews with prosecutors. “As is our policy, we intend to cooperate with all regulatory bodies, including providing copies of all documents requested by those bodies,” a company spokeswoman said in a statement.

Deutsche Bank, Mr. Trump’s primary lender since the late 1990s, received a subpoena last year from the district attorney and has said it is cooperating with the inquiry.

In court papers, the prosecutors have cited public reports of Mr. Trump’s business dealings as legal justification for their inquiry, including a Washington Post article that concluded the president may have inflated his net worth and the value of his properties to lenders and insurers.

Michael D. Cohen, the president’s former lawyer and fixer who turned on him after pleading guilty to federal charges, also told Congress in February 2019 that Mr. Trump and his employees manipulated his net worth to suit his interests.

“It was my experience that Mr. Trump inflated his total assets when it served his purposes, such as trying to be listed among the wealthiest people in Forbes, and deflated his assets to reduce his real estate taxes,” he said in testimony before the House Oversight Committee.

Mr. Trump’s supporters have noted that Mr. Cohen pleaded guilty in 2018 to lying to Congress and accused him of lying again to earn a reduced prison sentence.

The Trump Organization’s lawyers are also likely to argue to prosecutors that Mr. Trump could not have duped Deutsche Bank because the bank did its own analysis of Mr. Trump’s net worth.

Over the years, employees and executives inside the bank thought that Mr. Trump was overvaluing some of his assets by as much as 70 percent, according to current and former bank officials. Deutsche Bank still decided to lend Mr. Trump’s company hundreds of millions of dollars over the past decade, concluding that he was a safe lending risk in part because he had more than enough money and other assets to personally guarantee the debt.

The prosecutors’ interviews with the employees was not the only recent activity in the investigation. Last month, The Times reported that Mr. Vance’s office had subpoenaed the Trump Organization for records related to tax write-offs on millions of dollars in consulting fees, some of which appear to have gone to the president’s daughter Ivanka Trump.

According to people with knowledge of the matter, the subpoena sought information about fees paid to TTT Consulting L.L.C., an apparent reference to Ms. Trump and other members of her family. Ms. Trump was an executive officer of the Trump companies that made the payments, meaning she appears to have been paid as a consultant while also working for the Trump Organization.

Mr. Garten, the Trump Organization’s general counsel, argued in a statement at the time that the subpoena was part of an “ongoing attempt to harass the company.” He added that “everything was done in strict compliance with applicable law and under the advice of counsel and tax experts.”

Mr. Vance’s investigation has spanned more than two years and shifted focus over time. When the investigation began, it examined the Trump Organization’s role in hush money payments made during the 2016 presidential campaign to two women who claimed to have had affairs with Mr. Trump. Prosecutors were examining how the company recorded a reimbursement to Mr. Cohen for one of the payments. Mr. Cohen pleaded guilty to federal campaign finance violations for his role in the scheme.

A state grand jury convened by Mr. Vance’s office heard testimony from at least one witness about that issue last year, according to a person with knowledge of that testimony, but the payments have receded as a central focus of the inquiry.

Michael Rothfeld contributed reporting.