The next Republican debate on Wednesday could be the last one sponsored by the Republican National Committee in the 2024 primary race, with the party considering debate rule changes that would open the door to more onstage clashes but also diminish the fanfare around them.

The debate in Tuscaloosa, Ala., comes as Nikki Haley, the former United Nations ambassador, is trying to assert herself as the main rival to former President Donald J. Trump, after months in which Gov. Ron DeSantis of Florida has ceded ground. The R.N.C. is weighing a proposal to end its demand that candidates participate exclusively in the party’s debates, with a final decision expected this week.

Few have been happy with how the debates, which are overseen by the R.N.C., have unfolded so far. Mr. Trump has boycotted them, dampening interest and lessening the stakes. His rivals have been forced to fight among themselves. And lower-polling candidates have steadily been pushed out by rising thresholds to qualify.

Debates are traditionally the marquee events of a presidential primary contest, with voters eagerly tuning in to watch the candidates disagree on policy and vie for their support. But the Republican front-runner’s stubborn absence this election cycle has robbed them of much of their drama.

The debate on Wednesday will feature four candidates, the R.N.C. announced on Monday evening: Ms. Haley, Mr. DeSantis, the entrepreneur Vivek Ramaswamy and former Gov. Chris Christie of New Jersey, who appeared to have reached the polling requirement over the weekend as party officials met on Monday to approve a final poll that would allow him to qualify.

“The fourth debate is another fantastic opportunity for our Republican candidates to share our winning agenda with the American people,” Ronna McDaniel, the party chairwoman, said in a statement.

The party had previously signaled plans to hold forums in January in both Iowa and New Hampshire before those states’ nominating contests. Now, those debates may not happen as events sponsored by the party, according to four people involved in the process, though no final decisions have been made. The party could also still sponsor future debates even after stripping away the exclusivity requirement. Other news outlets have continued to engage in talks to hold debates.

The debate rule change idea was presented last week to the R.N.C.’s debate committee by David Bossie, who has led that group and was a former top political aide to Mr. Trump. The proposal was first reported by The Washington Post.

Multiple candidates have complained about the current limits, believing they have been denied the chance for exposure elsewhere. Still, some 2024 campaigns have been leery of the role that Mr. Bossie is playing for the party given his past close ties to Mr. Trump. The party’s debate committee will formally consider the proposal in a meeting after the debate in Alabama.

“As has been the process throughout the entire year, the debate committee will meet to decide the details of future debates,” said Emma Vaughn, a spokeswoman for the Republican National Committee, declining to answer specific questions.

Ratings for the debates have steadily shrunk. The first clash in Milwaukee, on Fox News, had 12.8 million viewers. The second debate, hosted by Fox Business, had 9.5 million. The third debate, on NBC News and other platforms, dwindled to 7.5 million, according to Nielsen figures.

And the fourth debate will be on a lesser-known platform than the first three, NewsNation. The moderators will be Elizabeth Vargas of NewsNation, the former Fox News anchor Megyn Kelly and Eliana Johnson of the Washington Free Beacon.

Mr. DeSantis, whose super PAC has been caught in a cycle of turmoil, has been aggressively seeking more opportunities in the national spotlight, including an unusual debate last week on Fox News with the Democratic governor of California, Gavin Newsom. And in a recent appearance on Newsmax, Mr. DeSantis said that network should get a debate. “Maybe as we go forward, maybe there will be more freewheeling debates,” he said.

Asked about the R.N.C.’s potential rules change, Andrew Romeo, a spokesman for Mr. DeSantis, said in a text message, “Ron DeSantis wants to debate Donald Trump and/or Nikki Haley in the early states regardless of who sponsors it.”

Ms. Haley’s team was more circumspect.

A spokeswoman for her campaign, Olivia Perez-Cubas, said in a statement: “Everyone knows Nikki Haley has shined in all the debates. We look forward to debating Donald Trump.”

It’s not clear that Mr. Trump will be debating anyone anytime soon, coasting on his polling dominance despite four criminal indictments and 91 felony counts.

The former president has boycotted all of the debates to date, arguing that it makes little sense for him to give rivals who are so far behind him any platform to hit him. Even as his campaign hopes for as many debates as possible in a general election against President Biden, he and his team have publicly called for the Republican Party to cancel its remaining debates, targeting the potential Iowa one in particular.

Previously, the party has squashed efforts for candidates to debate one another. At one point, Mr. Christie and Mr. Ramaswamy scheduled a debate on Fox News to gin up interest in their candidacies, but the party said it would violate the pledge.

“Trump allies in the RNC put an end to it,” Mr. Christie complained on social media. “Nothing new… Party bosses doing everything possible to keep Trump in power.”

Mr. Ramaswamy, meanwhile, used the last debate to attack Ms. McDaniel, the party chairwoman, and later circulated a petition to fire her. “Where is the accountability for years of losing: 2018, 2020, 2022 and now 2023?” he wrote on X, formerly known as Twitter.

His post did not mention Mr. Trump, who has been the face of the party during all of those elections. Mr. Ramaswamy has lavished praise on the former president even while running against him.

The criteria to make the party debates have significantly ratcheted up since August. The minimum threshold is now 6 percent in national or early-state polling, as well as 80,000 donors. The first debate required only 1 percent support.

Mr. Trump has been particularly keen on ending the debates before Iowa. The driver of his concerns isn’t clear. But Iowa was a particularly thorny state for him in early 2016, when he lost the caucuses after boycotting a debate in the state hosted by Fox News.

Citing Mr. Trump’s substantial polling lead, Steven Cheung, a campaign spokesman, said, “He’s going to be the nominee, so it’s time for everyone to get behind him.”