Utah Republicans are set to meet Saturday to decide who they would like to appear on the ballot in the state’s upcoming primary, a process that will signal which of the candidates the party is favoring.

In Utah, there are two ways that candidates can gain ballot access in a primary. They can either gather signatures and petition for access, or the state party can place them on the ballot.

Three candidates in the GOP field have submitted the requisite signatures to appear on ballots regardless of the party’s choices. According to a Utah State University political scientist, Damon Cann, this means that the convention this year serves “more of a winnowing function.”

Republicans and Democrats are meeting on Saturday to choose which candidates they would like to place on the state primary ballots. Their choices could give an indication of who the party is favoring and who is likely to be the next senator representing Utah.

The core question looming over the party conventions is whether the GOP will choose to put forward a candidate who follows in the path of Senator Romney, who is retiring, or Utah’s other lawmaker in that body, Senator Lee.

The contrast between the two Republican senators is sharp. On one hand, Mr. Romney is emblematic of a pre-Trump Republican Party and one of President Trump’s few critics within the ranks of Republican elected officials.

Mr. Lee, on the other hand, is far less critical of the former president in public and often publicly sides with members of the far-right House Freedom Caucus on issues ranging from national security to the debt ceiling.

“None of these candidates are running saying, ‘I will be just like Mitt Romney,’” Mr. Can says. “Usually in an open seat you have someone saying that they will be the heir to the incumbent.”

Potential favorites in the nine-candidate field to get the nod from the state party include a former speaker of the state’s house, Brad Wilson, and Congressman John Curtis.

Mr. Curtis has positioned himself between Messrs. Romney and Lee, telling the Idaho Capitol Sun, “I have a lot of respect for both of them, but I just don’t think I’ve modeled myself after either.” Mr. Curtis has portrayed himself as an effective legislator and as a top Republican on the topic of climate change, founding the Conservative Climate Caucus.

Mr. Wilson is attempting to parlay his reputation as a conservative state house speaker into a successful Senate campaign, also positioning himself between Messrs. Romney and Lee ideologically. Mr. Wilson had also racked up the endorsement of more than 60 Utah lawmakers before Mr. Romney announced that he would not seek re-election this year.

“I am honored and encouraged to have the support of so many leaders from all corners of this great state,” Mr. Wilson said in a statement. “Utah needs a bold, conservative fighter in the U.S. Senate and I am humbled at the support and encouragement we’ve received so quickly.”

The most prominent acolyte of Mr. Trump’s in the race is the mayor of Riverton, a city of 45,000 in the Salt Lake City area, Trent Staggs. While Mr. Wilson enjoys the support of state officials, Mr. Staggs has courted endorsements from online conservative personalities and loyalists of Mr. Trump.

According to Mr. Cann, Mr. Staggs has tailored his campaign to court Republican Party insiders, who tend to be even more ideologically conservative than GOP primary voters.

The last time Mr. Romney appeared before the convention, he was booed by the crowd — an indication that party insiders are more Trump-friendly than even GOP voters there.

 “Utah is so unique in the country,” Mr. Cann says. “It’s as Republican of a state as you find in the United States but even among Republicans support for Donald Trump is lower — I’m not going to say it’s low, but it’s lower than it is in comparable states.”

Personalities including Arizona’s Kari Lake, a conservative influencer, Charlie Kirk, and a failed presidential candidate, Vivek Ramaswamy, have all endorsed Mr. Staggs.

Congressman Matt Gaetz and Senator Tuberville have also advocated for Mr. Staggs, who has independently campaigned at Mar-a-Lago and CPAC, making him a potentially formidable primary candidate even if he doesn’t get the party’s nod.

“I’m not just somebody going out there trying to pick up any old endorsement,” Mr. Staggs told the Salt Lake Tribune of his campaign. “These are intentional. These are folks that I want to be able to say, ‘I’m going to emulate their type of fire and energy and ability to push back against the establishment.’”

Before entering politics, Mr. Staggs was the president at a multi-level marketing company, Regeneca, best known for male enhancement herbal remedies like RegenErect and RegeneArouse.

Whichever of the 10 candidates succeeds in getting the party’s nod Saturday, Mr. Curtis, Mr. Wilson, and businessman Jason Walton are still guaranteed to appear on the primary ballot, meaning that there will still be a live primary after the convention.