Harvard University and the Trump administration are nearing a potentially landmark legal settlement that would see Harvard agree to spend $500 million in exchange for the restoration of billions of dollars in federal research funding, according to four people familiar with the deliberations.

Negotiators for the White House and the university have made significant progress in their closed-door discussions over the past week, developing a framework for a settlement to end their monthslong battle.

The talks could still collapse, as President Trump and senior Harvard officials need to sign off on the terms of the deal. The sides are still going back and forth over important wording in for a potential agreement.

But under the framework coming together, Harvard would agree to spend $500 million on vocational and educational programs, three of the people said. That figure, currently penciled in to be paid out over years, would meet a demand from President Trump that Harvard spend more than double what Columbia University agreed last month to pay. It would also satisfy Harvard’s wish that it not pay the government directly, as Columbia is doing.

Harvard would also make commitments to continue its efforts to combat antisemitism on campus, two of the people said.

In return, Harvard — one of the largest recipients in higher education of federal research money — would see its research funding restored and avoid the appointment of a monitor, a condition the school has demanded as a way to preserve its academic independence, according to two of the people.

The Trump administration would also end its widening number of investigations into the university, including ones conducted by the Justice Department and another inquiry that the Commerce Department announced on Friday. The deal would also stop attempts by the Trump administration to block Harvard from enrolling thousands of international students, according to three of the people.

The stakes for reaching a deal are high for both Harvard and the administration. A deal would allow Mr. Trump to claim that Harvard forked over $500 million amid pressure from him. For Harvard, the deal would allow the school to remain one of the most robust higher education institutions in the country.

Harvard has insisted that any settlement must not jeopardize its academic freedom, and Mr. Trump has taken a keen interest in the details.

The people with knowledge of the deliberations spoke on the condition of anonymity because they did not want to be identified discussing talks that are supposed to remain confidential.

Harvard declined to comment.

Harvard has spent the last four months at the forefront of the opposition to the Trump administration’s pressure campaign against higher education. It is the only school that has sued after the administration targeted it with explicitly punitive funding cuts.

A settlement between the White House and the nation’s oldest and wealthiest university would reverberate throughout academia and could shape how other schools respond to Mr. Trump’s tactics. Last week, the administration proposed that the University of California, Los Angeles, pay more than $1 billion to reach a settlement with the government.

Some terms in an agreement with Harvard are expected to be similar to ones included in a deal Brown University struck with the White House in late July, such as a provision intended to guard academic independence.

Brown’s deal included language that barred the government from dictating curriculum or the content of academic speech. It also touched on several other issues central to the administration’s attacks on higher education, including transgender athletes who play on women’s teams and the treatment of Jewish students in the wake of the protests against the Gaza war.

Brown will have to ensure locker rooms and bathrooms are reserved for female athletes, perform outreach to Jewish groups and hire an external group to conduct campus climate surveys, for example.

Although Harvard officials welcomed many of the Brown deal’s nonfinancial conditions, they were stunned that the university agreed to pay only $50 million over a decade as they were being pressed to cough up 10 times that sum.

But with the beginning of the school year approaching, negotiators have accepted that they will have to pay $500 million to strike a deal, and instead focused on how payments would be structured.

One potential sticking point could be the government’s access to admissions data, especially numbers involving applicants’ race. The administration was seeking a stipulation in the deal that would require Harvard to release detailed admissions data, including on race and gender as well as grade point averages and standardized test scores. That would be consistent with an executive action that Mr. Trump signed last week, forcing schools nationwide to give the government similarly detailed data.

Brown and Columbia, as part of their deals, both agreed to supply the administration with that information, something conservatives have sought in an effort to prove that elite schools have disregarded a recent Supreme Court decision banning affirmative action.

May Mailman, a White House adviser driving the negotiations with top universities, suggested in a recent interview that Harvard’s inclination to provide data surrounding its consideration of race in admissions would be a factor in the government’s willingness to sign off on a deal.

It was not clear on Monday how any agreement between the government and Harvard would resolve that demand, which the university has viewed as overly invasive. It was also not clear when Mr. Trump would be briefed on the potential agreement.

The White House and the university opened negotiations in June, each seeking an offramp from a clash that began with accusations of antisemitism and became a battle over academic independence and the specter of federal overreach.

The dispute between Harvard and the White House erupted in the spring after the Trump administration inadvertently sent the university a list of demands that would reshape student and academic life, including surveys of the student body’s political ideology, audits of the curriculum and a reduction in the influence of untenured faculty. The university quickly refused them, and the administration responded hours later by starting to freeze billions of dollars in research funding.

Harvard, like other top schools, depends on that funding and has done so for decades. The university took the administration to court in April, arguing that assorted government demands threatened Harvard’s constitutional rights. The school also asserted that the government had violated its own procedures when it hastily cut off research funding.

A federal judge in Boston appeared skeptical of the government’s efforts when she heard arguments in the lawsuit in July. Both the administration and Harvard have asked the judge to rule in their favor without a trial, but she has not yet issued a ruling.

Harvard officials have been combative, depicting their fight against the Trump administration as a vital crusade. But behind closed doors, they have been wary of a sustained war with the White House.

Even if Harvard prevailed in court, some inside the university have argued, the administration could continue to pelt the school with investigations and subpoenas while, over time, bleeding it of research funding through more standard protocols. To them, a settlement was an unappealing but essential outcome.

Although Harvard has an endowment valued at roughly $53 billion, much of it is restricted, meaning that university officials are limited in how they may use it. And the school has shown signs of financial strain as federal research funding has evaporated.

University leaders warned last month that the blitz of actions from Washington, including an increase in the excise tax on endowments, could blow a nearly $1 billion annual hole in Harvard’s budget.

Still, proponents of a possible deal have faced fierce resistance on Harvard’s campus in Cambridge, Mass.

There, faculty members and students have warned that an agreement with the White House would amount to capitulation and that Mr. Trump could not be trusted to honor any arrangement over the long term. Given those concerns, Harvard’s negotiators have pressed the administration in recent weeks, insisting that any resolution of their fight be structured as a legal settlement. A legal settlement would make it more difficult for the administration and Mr. Trump to change the terms after the fact.

Oliver Hart, an economics professor at Harvard who won a Nobel Prize for his work on contract theory, said in an interview last month that the university should ensure there is a clear process for resolving disputes.

“I would spell out what happens if a party feels the agreement is not being honored,” Dr. Hart said. Referring to the government, he added, “If they have so many things up their sleeve, they’re going to have those things up their sleeve once you’ve agreed on a deal.”