The New York attorney general's office has rebuffed an offer from Donald Trump's lawyers to settle a contentious civil investigation into the former president and his family real estate business, setting the stage for a lawsuit that would accuse Trump of fraud, according to three people with knowledge of the matter.

The attorney general, Letitia James, is also considering suing at least one of Trump's adult children, the people said. Ivanka, Eric and Donald Trump Jr. have all been senior executives at Trump's company, the Trump Organization.

The likelihood of a lawsuit grew this month after James' office rejected at least one settlement offer from Trump's lawyers, the people said. While the Trump Organization for months has made overtures to the attorney general's office — and the two sides could still reach a deal — there is no indication that a settlement will materialize anytime soon.

James, a Democrat who is running for reelection in November, is focused on whether Trump fraudulently inflated the value of his assets and has mounted a 3 1/2-year inquiry that has cemented her as one of the former president's chief antagonists. Trump, who has denied all wrongdoing and derided the investigation as a politically motivated witch hunt, has fired back at her, filing an unsuccessful lawsuit to block her inquiry and calling James, who is Black, a racist.

A lawsuit from James would supercharge their drawn-out battle, offering her an opportunity to deliver a significant blow to the former president and his business, which she vowed before taking office to "vigorously investigate." If the case goes to trial and Trump loses, a judge could impose financial penalties and restrict the former president's business operations in New York — all potentially in the midst of a 2024 presidential campaign that he is expected to join.

Yet while many politicians might shrink from a government lawsuit, Trump has a long track record of leveraging law enforcement scrutiny to energize his base while portraying himself as a political martyr. And James is not assured victory if the lawsuit proceeds to trial; if it does, Trump might deploy his favored legal tactics — delay and litigate every last detail of a case — to stall in the coming months or years.

James is hardly the only one investigating Trump, whose final weeks in office are under the microscope in at least three separate criminal investigations. The FBI last month searched his home and club in Florida as part of a federal investigation into his removal of sensitive material from the White House; federal authorities recently seized the phones of two of his close advisers and sent subpoenas to dozens of his aides in an inquiry into Trump's efforts to reverse his election loss; and a Georgia district attorney has cast a sprawling net in an investigation into potential election interference by the former president and his allies.

Trump has denied all wrongdoing, and it is unclear whether any of these investigations will result in charges against the former president. His company, however, is already under indictment on an unrelated case.

The Trump Organization is set to go on trial next month for criminal tax charges in Manhattan, a case that could expose the company to steep financial penalties if it is convicted. And although Trump was not accused of wrongdoing in that case, in which the attorney general's office is also participating, his longtime chief financial officer recently pleaded guilty to participating in the tax scheme and agreed to testify at the company's trial, giving prosecutors in the Manhattan district attorney's office the upper hand.

Trump moved to Florida after leaving the White House, but his company remains headquartered at Trump Tower in midtown Manhattan. The company also owns or manages an array of properties in New York: a hotel overlooking Central Park, three golf clubs and several commercial real estate and residential towers.

It is possible that James, as part of her lawsuit, could seek to curtail Trump's Manhattan real estate portfolio, although she has given mixed signals publicly about what sort of punishment she will seek to impose.

The two came face to face last month, when Trump declined to answer her questions under oath in the course of a four-hour court-ordered deposition. Trump invoked his Fifth Amendment rights more than 400 times during the session, breaking his silence only to attack James as a "renegade prosecutor" who he said is leading a witch hunt against him, people with knowledge of the matter have said.

His decision to stay silent may have handed the attorney general some additional leverage: In civil cases, refusing to answer questions can, in some instances, be held against defendants at trial.

Eric Trump, who ran the company when Trump was in the White House, invoked his Fifth Amendment rights more than 500 times in a 2020 deposition with James' office. When Donald Trump Jr. and Ivanka were interviewed in hourslong sessions under oath this summer, they responded to questions. There is no indication that they played a role in setting the value of Donald Trump's assets, but they were senior officers in the company for many years.

James' civil inquiry is centered on whether Trump's annual financial statements falsely inflated the value of his assets — golf courses, hotels and commercial real estate — so that he could secure favorable loans and other financial benefits. That area of focus overlaps with a separate criminal investigation from the Manhattan district attorney's office, which had been moving toward an indictment of Trump early this year before prosecutors developed concerns about proving that he intentionally fabricated the assets' value.

The district attorney, Alvin Bragg, has said that his office is continuing to investigate Trump, an inquiry that is separate from the tax charges against the Trump Organization that his office is taking to trial next month.

Trump's silence under oath at his deposition stemmed in part from the existence of Bragg's investigation. His lawyers feared that any misstatement — or self-incrimination — could have breathed new life into that inquiry, a person with knowledge of his thinking said at the time.

James, who does not have the authority to criminally charge Trump, had subpoenaed the former president in December to testify under oath and provide an array of documents to her office.

In January, James filed an unusual court document accusing Trump's company of engaging in "fraudulent or misleading" practices related to his annual financial statements, while adding that she needed to collect additional records and testimony before deciding whether to sue Trump or his company.

Trump fought the subpoena, but in March, a New York state judge ruled in favor of James, ordering the former president and Ivanka and Donald Trump Jr. to sit for questioning under oath.

In April, the same judge, Arthur F. Engoron, held Trump in contempt of court for not fully complying with James' subpoena for documents. The judge ultimately ordered Trump to pay $110,000.

In court papers, James has outlined the contours of a potential civil case against Trump and the Trump Organization related to his annual financial statements, accusing the company of repeatedly misrepresenting the value of its assets to bolster its bottom line.

Many of Trump's financial statements, the filing argued, were "generally inflated as part of a pattern to suggest that Mr. Trump's net worth was higher than it otherwise would have appeared." The filing cited what James' office believes were misleading statements about the value of Trump's golf clubs in Westchester County, New York, and Scotland, his flagship commercial property at 40 Wall St. in Manhattan and his penthouse triplex in Trump Tower.

The company provided these statements to lenders and insurers, the filing said.

Her case against him could be hard to prove. Property valuations are often subjective, and if James ultimately sues Trump, his lawyers would be likely to point toward the disclaimer in his financial statements saying that his accountants had not audited the valuations.

They also might argue that the Trump Organization submitted the statements to sophisticated financial institutions that conducted their own due diligence. In recent months, he paid off some of those loans, an outcome that funneled hundreds of millions of dollars into the coffers of his banks, making them an unsympathetic victim.

Trump also famously does not use email, so any instructions he might have given his employees about the financial statements are most likely not in writing. The lack of a damning email — or witness currently inside his company willing to testify against him — might make it somewhat difficult to show that he used his financial statements to defraud anyone.

But in a June podcast appearance, James expressed confidence that she would prevail.

"We all know that he used funny numbers in his financial documents," she said, adding, "And he got caught."

The preliminary settlement talks between James' office and Trump's lawyers began early this summer and have yet to gather much momentum, the people with knowledge of the matter said. James' office turned down the offer from Trump's lawyers, although they are expected to continue to try to negotiate in the coming days.

It is common for attorneys general to entertain settlement negotiations both before and after filing lawsuits.

A deal-breaker for Trump would be if James sought to shut down his business operations in New York. But in the same podcast appearance, James suggested that she might stop short of seeking what is sometimes called the "corporate death penalty," in which a judge orders the dissolution of a company.

"I don't want to go that far," James said. All she wanted to do, she added, was to ensure that Trump and his company understood that they could not use fraudulent valuations in the future. "​He needs to be held accountable," she said. "Him and his corporation."

Maggie Haberman contributed reporting.