As he dips his toe into politics, former big-time college football coach Tommy Tuberville has at least one element politicians covet: name recognition.

Mr. Tuberville is seeking Republicans’ nomination to run for Alabama’s Senate seat next year, and his campaign says its new polling shows he’s well-positioned, leading the potential field with 23%, ahead of former state Supreme Court Chief Justice Roy Moore at 18%.

U.S. Rep. Bradley Byrne has 16%, John Merrill, Alabama’s Republican secretary of state, polled at 7% and Republican state Rep. Arnold Mooney had 2%.

Eric Iverson, president and CEO of Moore Information Group, which conducted the poll, said Mr. Tuberville is not only well-known, but also benefits from being an outsider — with 65% of likely GOP primary voters preferring someone who has not spent years in office.

“Tuberville is the top choice of these voters as well,” Mr. Iverson said.

Chief Justice Moore and Mr. Merrill have not announced candidacies yet.

Mr. Mooney, 68, did not immediately respond to a request for comment.

Mr. Byrne, 64, downplayed the survey, saying it wasn’t surprising Mr. Tuberville’s internal polling gave him an advantage. He also said the poll was built strictly around name recognition.

Seth Morrow, the Byrne campaign manager, said they’ll grow as their candidate becomes better known.

“Our campaign has the resources and grassroots support to make sure voters across Alabama get to know Bradley and his record as a conservative reformer who supports President Trump and his effort to drain the swamp,” he said.

The poll did not give any hints as to whether Mr. Tuberville suffers for his association with the Auburn University Tigers, the football team he coached for years, including an undefeated season in 2004.

Such success can only come with victories in the Iron Bowl, the annual game between Auburn and the University of Alabama, a rivalry so vitriolic an Alabama fan was once convicted of poisoning beloved trees on the Auburn campus.

For now, though, he’s resonating with some voters.

“Tuberville just hit that nerve that reminded me of Trump,” said Donna Hamaker, a Republican from Huntsville. “I saw many similarities in Mr. Tuberville and President Trump. Not a politicians, an outsider, new perspective and wants to get things done. He’s conservative, tough on illegal immigration and would stand up to the establishment.”

Republicans are seeking to unseat Sen. Doug Jones, a Democrat who in 2017 captured the seat once held by Republican Sen. Jeff Sessions.

In that race Mr. Jones defeated Mr. Moore, long a controversial figure in Alabama who also found himself fending off various charges of improper behavior with young women from his days as a young prosecutor.

Although Mr. Moore has not revealed if he will run again in 2020, and his participation has been actively discouraged by President Trump and other Republicans, the former justice is widely expected to announce his candidacy by the end of June.

That would certainly complicate GOP efforts to unseat Mr. Jones, who is rated the most vulnerable U.S. senator by most political prognosticators.

Mr. Tuberville’s campaign poll found Mr. Moore would enter the race with a 48 percent unfavorable rating within the GOP.

The poll of 650 likely Republican primary voters was taken on June 11, and had a margin of error of plus or minus 4 percentage points.

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