Harvard University, battered by a devastating conflict with the Trump administration that has jeopardized its elite standing, is facing a problem as it weighs a possible truce with President Trump: how to strike a deal without compromising its values or appearing to have capitulated.

The conundrum has bedeviled law firms, tech and media companies and even one of the school’s Ivy League peers. According to three people familiar with the university’s deliberations, it is now shaping internal debates around the school’s freshly resurrected talks with the government. They spoke on the condition of anonymity because they did not want to be identified discussing negotiations that are supposed to be private.

Unlike many other powerful institutions that have struck bargains with Mr. Trump, Harvard, the nation’s oldest and richest university, spent much of this spring as the vanguard of resistance to the White House, credited by academic leaders, alumni and pro-democracy activists for fighting the administration and serving as a formidable barrier against authoritarianism.

Despite a series of legal wins against the administration, though, Harvard officials concluded in recent weeks that those victories alone might be insufficient to protect the university.

The internal discussions at Harvard are particularly fraught because among the sticking points with the Trump White House are issues of admissions, hiring and viewpoint diversity. Universities regard admissions and hiring as especially critical to academic freedom — a cornerstone that government oversight could dilute, compromising their independence and infringing on constitutional protections for speech. And Harvard officials are well aware that a deal with the Trump administration on anything related to the school’s academic independence could invite lasting anger from an already anxious faculty.

Also hanging over a potential deal between the president and Harvard are the ones that some of the most powerful institutions in the country made after Mr. Trump’s election in November.