A new poll shows former Rep. Trey Gowdy leading the Republican field in South Carolina's special U.S. Senate primary election, though he says he has no interest in running.

The death of Sen. Lindsey Graham, R-S.C., while seeking reelection triggered a special election to determine who will serve the next six-year Senate term. Gov. Henry McMaster appointed his sister, Darline Graham, to temporarily fill the seat until the winner is sworn in.

The poll from Peak Insights, a Republican-aligned firm and obtained by Politico, shows Gowdy would be the front-runner for the Republican primary, with 38% of the vote.

Rep. Ralph Norman, who has declared his candidacy, has 13% while Rep. Russell Fry, who also entered the race, has 9%.

Darline Graham also has 9%. The poll was conducted before Norman and Fry formally announced their candidacies.

Darline Graham was recently endorsed by President Donald Trump and announced she intends to run for a full term.

But Trump's endorsement appears to give her only a little boost. When respondents were told she had Trump's endorsement, her support improved to 16%, while Gowdy's numbers fell only to 35%.

Gowdy served four terms in Congress before declining to run for reelection in 2018. A spokesperson for Gowdy told Politico he "has not had any conversations about the open Senate seat and does not have any interest in it."

Peak Insights has previously polled for Sen. Tim Scott, R-S.C., who chairs the National Republican Senatorial Committee, Politico reported.

Scott pushed for Gowdy to be appointed to fill Lindsey Graham's seat and said he was recruiting him to run in the special election.

"I can't think of a better person that I think best represents the heart of South Carolina than Trey Gowdy," Scott said in an interview. "I'm trying to get him interested in it, but we'll see if that works out at all."

The survey of 900 people conducted July 18-July 20 has a margin of error of +/-3 percentage points.