COLUMBUS, Ohio — The prospect that former President Donald J. Trump might soon endorse the author and venture capitalist J.D. Vance in Ohio’s crowded Republican Senate primary race stirred confusion and anxiety on Friday, with some G.O.P. leaders mounting a last-ditch effort to persuade Mr. Trump against shaking up what has been a contentious and at times nasty campaign.

With the May 3 primary less than three weeks away, Mr. Trump has so far declined to weigh in, though the race’s top candidates have increasingly veered to the right in aggressive pursuit of his support. The tension and anticipation have been especially high ahead of a planned visit to the state by the former president on April 23.

Mr. Trump’s highly coveted endorsement could carry weight in a conservative-leaning state where 3.1 million people voted for the former president in November 2020, the highest number of votes ever garnered by a presidential candidate in Ohio. But it also carries risks for Mr. Trump given the open field and limited polling that shows Mr. Vance struggling to break through.

In other states, Mr. Trump’s endorsement in high-profile races has not yet proven decisive. In Georgia, his attempt to fuel David Perdue’s Republican primary challenge to Gov. Brian Kemp has largely been seen as underwhelming.

Few races across the country have captured Mr. Trump’s effect in Republican primaries in the way that Ohio’s Republican Senate campaign has, with candidates seeking to model themselves after the former president. Most of the contenders have railed against undocumented immigrants, and only one has recognized President Biden as the nation’s legitimate leader. Two nearly came to blows during a recent debate.

No candidate has emerged as a clear front-runner, and news reports this week about a possible Trump endorsement of Mr. Vance mobilized opponents against the move. The news appeared to have been leaked in an attempt to prevent the endorsement from happening; Republicans have grown familiar with the rhythms of Mr. Trump’s whims, and his penchant for responding to how he sees political developments playing out in news coverage.

Nonetheless, Mr. Trump was still leaning on Friday toward endorsing Mr. Vance, according to four people familiar with the conversations among Mr. Trump’s advisers who spoke on the condition of anonymity to discuss internal deliberations.

Many Republican county party leaders expressed frustration that Mr. Trump might select Mr. Vance, the author of the best-selling 2016 memoir “Hillbilly Elegy.” They noted that he had spent much of his life in San Francisco and had been critical of Mr. Trump even as they worked to elect him.

“He is the guy who worked against Trump and spoke against Trump and told everybody he didn’t vote for Trump,” said David Johnson, the chairman of the Columbiana County Republican Party, who has endorsed Jane Timken, a former chairwoman of the Ohio Republican Party who is now running for Senate. “He is a very bright guy and well spoken, but the concern is he wouldn’t carry the Republican Party Trump base in Ohio, and you have to have this to win.”

Mr. Johnson helped circulate a letter, signed by more than three dozen Republican county and state committee leaders, that was addressed to Mr. Trump and called on him to block the endorsement. It states that Mr. Vance is not a registered Republican and provides Mr. Trump with a list of negative comments that Mr. Vance has made against him in the past, including calling him “another opioid” in 2016 and saying that he hoped Mr. Trump would be “soundly defeated” that year.

“While we were working hard in Ohio to support you and Make America Great Again, J.D. Vance was actively working against your candidacy,” the letter says. “He referred to your supporters as ‘racists’ and proudly voted for Evan McMullin in 2016.”

Jeff Mangun, the chairman of the Carroll County Republican Party, who signed the letter and has not endorsed anyone in the Senate primary, echoed the concerns about a potential Trump endorsement of Mr. Vance. “The best-case scenario is for him to remain neutral, but even if he were to endorse someone, I would prefer it would be someone else,” Mr. Mangun said. “I just don’t think it’s a good fit.”

Asked for comment, including about the accusation that Mr. Vance is not a registered Republican, a spokeswoman for the Vance campaign pointed to polling that showed Mr. Vance and Josh Mandel, a former Ohio state treasurer, neck and neck at the top; a tweet from one Republican Party county chairman denying that he had signed the letter; and another tweet from the anti-abortion group Ohio Right to Life PAC that expressed support for a Trump endorsement of Mr. Vance.

In stump speeches, Mr. Vance has been quick to address the criticism that he has not always been a Trump loyalist, often saying that the best policy is honesty.

“I didn’t like Trump six years ago,” he told a small crowd of supporters this week at a brewery in Hilliard. “I did not think he was going to be a good president. I was very happy to be proven wrong.”

He added, “I was very proud to support the president over the past several years.”

Mr. Trump is said to have been moving toward Mr. Vance for some time, according to the four Republicans familiar with his advisers’ discussions. He has been encouraged by a range of allies and donors, including the billionaire Peter Thiel, who is a primary financial backer of Mr. Vance. The Fox News host Tucker Carlson, who is influential with members of Mr. Trump’s base, has also spoken favorably about Mr. Vance on his prime-time show.

Mr. Vance’s opponents began attacking him over his lack of Trump fealty early, and have spent nearly $2.8 million in television and digital ads since February, according to an analysis by the media tracking firm AdImpact.

Many Republicans in Ohio have been waiting for Mr. Trump to endorse a Senate candidate, saying it would help them make a decision. But with voting already underway, some voters at Republican events this week had already cast their ballots or had at least made up their minds.

At a gathering for Ms. Timken in Athens on Thursday, at least one voter said Mr. Trump’s backing was significant but not a game changer. “If she wasn’t a Trump supporter, I probably wouldn’t support her,” said Amy Karr, 50, an accountant in Racine. But Ms. Karr said she planned to vote for Ms. Timken regardless of whom Mr. Trump endorsed.

Ms. Timken said she was the only Republican candidate for Senate whom the former president had endorsed in the past, when she was in the running for chair of the Ohio Republican Party.

“I know there’s rumors swirling around, but there seems to be rumors swirling around all the time,” she said. “Look, President Trump is very popular with Republican primary voters. But every day I’m out earning the vote of Ohioans, and they’re the ones who are going to make this difference in this race.”

Jazmine Ulloa reported from Columbus, Ohio, and Maggie Haberman from New York.