The dean of Yale Law School and some members of its faculty are trying to stop a settlement between the university and the Trump administration, warning that an agreement could jeopardize Yale’s independence, according to two people familiar with the deliberations.

The dean, Cristina M. Rodríguez, and a group of law school faculty members have quietly lobbied top Yale leaders in recent days, arguing that the Trump administration cannot be trusted and that settling would threaten the rule of law and the university’s reputation. They have even explored whether the law school could be excluded from any settlement with the federal government.

So far, Yale’s leaders have continued to move forward with negotiations with the administration, according to one of the people. Yale’s leaders have privately contended that they may need to strike a deal to ensure the university continues to receive federal funding, the person said.

The Justice Department has been conducting an inquiry into Yale’s admissions practices for undergraduate programs, its medical school and the law school, expanding the Trump administration’s efforts to remake American higher education.

The Justice Department has already accused Yale of illegal discrimination in medical school admissions. But the investigation into the law school has not been completed. Some at the school are recoiling over the prospect of settling before the government has accused Yale of wrongdoing — and before Yale has had a chance to contest any findings.

The people familiar with the deliberations spoke on the condition of anonymity to describe internal discussions. Through a spokesperson, Ms. Rodríguez, who became dean this year, declined to comment.

The dean’s concerns mirror those of others at Yale, where students and alumni have been openly pressuring the university’s president, Maurie McInnis, not to sign an agreement with the Trump administration. Many of those people fear that a settlement would damage the university’s reputation.

Citing longstanding practice, a spokeswoman for Yale, Karen Peart, said the university would not discuss any ongoing legal matters.

“That said, we stand firm in the university’s commitment to students’ free expression, academic freedom, and Yale’s ability to determine who is admitted in accordance with the law,” she wrote in an email. “We take inspiration from our current students and our thousands of alumni. Their wide range of perspectives, talents, aspirations and experiences have deepened our community, and their achievements have confirmed the strength of Yale’s admissions.”

Asked about campus opposition to a potential settlement, Ms. Peart said, “We are committed to supporting the members of our community in their beliefs and values.”

The White House referred a request for comment to the Justice Department, which did not immediately respond.

The Trump administration has used pressure tactics, from funding cuts to legal threats, to secure settlements with six elite universities and thrust others into chaos, a pattern that many in academia regard as a dangerous precedent for political interference, especially at private institutions.

Some inside the law school believe an effort to reduce or eliminate funding would warrant a court challenge much like the one that Harvard brought last year to restore grant money.

Although students, alumni and professors have often disagreed openly with administrators over how to respond to President Trump, it is rare for debate among university leaders to come into public view.

But word of Ms. Rodríguez’s opposition has spread through Yale in recent days, according to the two people. Ms. Rodríguez was also examining whether it was possible for the law school, long known for its independence within Yale, not to be included in an agreement with the government.

It is not clear whether Yale or the government would agree to such an arrangement.

The government has not publicly accused Yale of wrongdoing in undergraduate or law school admissions. In May, it said Yale’s medical school had discriminated against white and Asian applicants and illegally favored Black and Hispanic students. In a letter announcing its findings about the medical school, the Justice Department told a lawyer for Yale that it wanted to reach “a voluntary resolution agreement with the university to ensure that admissions practices are brought into legal compliance.”

The New York Times reported in June that the Justice Department’s inquiry went beyond the medical school and that the university was considering a broader settlement. In the wake of the article, Ms. Rodríguez, who worked with the Justice Department during the Obama and Biden administrations, moved to register her concerns. It is unclear, though, whether her views are shaping Yale’s dealings with the federal government.

Robert C. Post, the law dean at Yale between 2009 and 2017, said in an interview that university leaders confronting thorny legal issues did not usually engage with the law school’s experts. But he said he wished they would.

“If they’re going to change our admission practices by way of a legal agreement, I would have hoped they would consult with us, and I would hope they would take our advice about what’s legally required and not and when we should fight legally and not,” said Dr. Post, who remains on Yale’s faculty. “But so far, to my knowledge, that hasn’t happened to law school faculty.”

Legal experts besides Ms. Rodríguez have also expressed skepticism.

A memo opposing a potential settlement — prepared by Serena Mayeri and Amanda Shanor, who earned law degrees from Yale and now teach constitutional law at the University of Pennsylvania — has been circulating on campus. Addressed to Dr. McInnis and Yale’s general counsel, the nine-page document argued that other schools’ settlements had not proven all that favorable and included troubling requirements.

For example, Dr. Mayeri and Dr. Shanor said that agreements had bound “schools to vague, shifting and contradictory definitions of prohibited conduct that go far beyond and may violate established law.” And, nodding to provisions requiring regular certifications from university officials about their schools’ compliance with settlement terms, they cautioned that “creation of possible personal civil and criminal liability for university leaders functionally ensures ongoing federal oversight and control.”

Dr. Mayeri and Dr. Shanor acknowledged that Yale was facing “an unenviably difficult situation.” But, they added, “the existential nature of the threat is a reason not to consent to deals that amount, at best, to conditional reprieves of uncertain duration and value.”

Dr. Post offered a similar warning, saying that the Trump administration “tends to take advantage of whatever contracts it enters into.”

Some with ties to the law school are also harboring significant concerns about Yale’s decision to use the law firm McGuireWoods for the talks with the government. The firm represented the University of Virginia in negotiations last year that led to an agreement with no financial penalties but included policy concessions.

James E. Ryan, the Yale alumnus who resigned from the Virginia presidency under Justice Department pressure last year, wrote in a November letter that he had developed misgivings about the approach McGuireWoods adopted for the extensive federal inquiry into Virginia.

Referring to McGuireWoods lawyers, Mr. Ryan wrote that he did “not know if they were exercising their independent judgment or receiving directions from a board member and/or the attorney general’s office.” Jason Miyares, a Republican allied with Mr. Trump, was Virginia’s attorney general at the time.

Neither the firm nor Mr. Miyares responded to requests for comment.

Some students at Yale, like many of their counterparts on other Ivy League campuses, have also aired objections to a potential settlement with the Trump administration.

“Our rights, our classmates, our lectures, our speech and our independence are not, and never have been, valid bargaining chips,” Michelle Jimenez, the vice president of the Yale College Council for the coming academic year, said in a video released over the weekend.

And on Monday afternoon, the alumni group Stand Up for Yale sent a letter to Dr. McInnis, asserting that a settlement would signal “that Yale doesn’t stand by the work of its attorneys, the judgment of its admissions officers or the brilliance of its students, and that it’s eager to betray its values for a dangerous illusion of security.”

More than 2,700 people had signed.

Michael C. Bender and Mark Arsenault contributed reporting.