Former Rep. Jason Chaffetz just barely retired from politics, but he’s become the “very early” front-runner in the next race for Utah governor in 2020.

The Republican received the most support — 24 percent — among a list of potential candidates in a new Dan Jones & Associates poll for The Salt Lake Tribune and the Hinckley Institute of Politics.

Not far behind is Democratic Salt Lake County Mayor Ben McAdams, with 20 percent — but he was included in the poll before he chose recently to run next year in the 4th Congressional District against Rep. Mia Love. Still, he could opt to run for governor in the race that occurs two years later.

Lt. Gov. Spencer Cox had 11 percent support. Others include businessman Josh Romney (son of Mitt Romney), 9 percent; 3 percent each for House Speaker Greg Hughes and businessman Spencer Eccles; and 2 percent for Greg Miller, former CEO of the Larry H. Miller Group and Utah Jazz.

Incumbent Gov. Gary Herbert, who has served since 2009, has said he does not plan to seek re-election.

Jones, the pollster, said the new survey coming three years ahead of the election “is very early and is mostly about name recognition at this point. But those candidates who are there are very formidable.”

Chaffetz — who resigned from Congress on June 30 to become a contributor at Fox News, a fellow at Harvard and to write a book — said he is flattered to lead the pack for now, but added he has made no decision about whether to run for governor.

FILE - In this May 24, 2016, file photo, Rep. Jason Chaffetz, R-Utah, testifies on Capitol Hill in Washington. Forty-one Secret Service employees have been disciplined for reviewing private agency records, including a failed job application of Chaffetz who was leading a congressional probe of the agency. (AP Photo/Andrew Harnik, File)

“That decision is a few years off,” he said. “I stepped down from office not as a precursor to run for something else, but to shift gears in my life.” He said he is enjoying a new lifestyle that allows more time for family.

“It’s a better mix for me. I love it. I have no regrets in stepping down. I always said I wanted to get in, serve, and get out. But maybe I will get back in at some point.”

He called running for governor “a definite maybe,” and said “if the situation is right, I very well might do that.” He again quickly added that “I’m not gunning for any political office right now.”

He has $284,000 remaining in his campaign fund, according to his latest disclosure forms, which could provide a nice financial head start if and when he chooses to run for office again.

Meanwhile, McAdams enjoyed a fairly strong showing in the early poll — especially for a Democratic Salt Lake County official in a statewide survey that goes well beyond his local base of power.

He declined comment on the poll question about whether he would consider running for governor, now that he is focused on running for Congress. His name often has come up as a potential candidate for governor or the U.S. Senate.

Steve Griffin / The Salt Lake Tribune Salt Lake County Mayor Ben McAdams meets with the Salt Lake Tribune Editorial Board at the paper's offices in Salt Lake City Monday September 19, 2016.

University of Utah political science professor Matthew Burbank said the moderate, affable McAdams often is mentioned as a candidate for many major offices by Democrats in heavily Republican Utah “because he’s kind of the one person they can look at and say he might have a chance.”

Among unaffiliated voters — a group in Utah that is larger than Democrats, and not far behind Republicans — McAdams actually was the leader in the poll. He attracted 24 percent support among that group, compared to 19 percent for Chaffetz.

Burbank said Cox’s showing with 11 percent support in the poll isn’t too surprising in a poll largely about name recognition, because many people often do not know who holds the office of lieutenant governor. Cox himself often jokes about it.

“But if you are talking about a position to help prepare someone to be governor,” Burbank said, “that’s the position to be looking at.”

Cox — who commutes 200 miles daily between his farm in Fairview and the Capitol in Salt Lake City — said he is leaning toward running for governor, but has made no final decision.

(photo courtesy Spencer Cox) Lt. Governor Spencer Cox works on his farm near Fairview.

He added that his work as lieutenant governor has taught him that doing the job correctly is difficult and not glamorous, and he would be committed to do the tough work that needs attention.

“We would be all in and we would work our guts out and we would leave everything on the table,” if he runs, he said.

Herbert — who also was a lieutenant governor — said Cox has had the same sort of preparation to be governor that he did. Herbert said Cox “has the talent and the capability to be a good governor.”

Hughes is often mentioned as a potential gubernatorial candidate, but House speakers generally have had bad luck in making that jump. Only former Gov. Norm Bangerter did that in recent history (1984).

Al Hartmann | The Salt Lake Tribune Speaker of the House Greg Hughes strikes the gavel Monday Jan. 30 to start the second week of the Utah 2017 Legislature.

Among other House speakers who ran for governor but lost are Marty Stephens, Nolan Karras and Jim Hansen (who ran after he served 22 years in Congress). Also, former House Speaker Becky Lockhart was widely believed to be preparing for a run for governor against Herbert when she died from a rare brain disease in 2015.

The new poll interviewed 605 registered voters between Oct. 10 and 13. Its margin of error is 3.98 percentage points, plus or minus.