"I haven't been asked," he said about rumors Gov. Rick Scott might want him to fill the position vacated by Jennifer Carroll.
She stepped down in March, the same day she was questioned by law enforcement officials about her association with Allied Veterans of the World. The St. Augustine-based nonprofit is at the center of a $300 million federal racketeering probe.
Thrasher is a Republican representing District 6, which covers St. Johns, Flagler and Putnam counties and of Volusia county.
Asked how he would respond if Scott asked, Thrasher said: "I don't think that's going to happen."
Thrasher joined Scott and Clay County executives and elected officials Wednesday to announce that railroad signalization company RJ Corman Railroad Group LLC had chosen Clay County for a 58-job operation.
It has leased space in the Fleming Island Business Park. The company is based in Nicholasville, Ky.
The announcement came at the Thrasher-Horne Conference Center in Clay County, named in part for Thrasher, a longtime former Clay elected official and former speaker of the House of Representatives.
A former chairman of the Republican Party of Florida, he also served as co-chair for the George W. Bush for President campaign in 2004.
Carroll, who was a Fleming Island resident in Clay County, resigned March 12. A consulting firm owned by Carroll did work for Allied Veterans while she was in the House. She also appeared in a commercial for the group.
In a statement released when Carroll resigned, Scott Chief of Staff Adam Hollingsworth said she stepped down "to keep her former affiliations with the company from distracting from the administration's important work on behalf of Florida families. She made the right decision for the state and her family."
State Sen. John Thrasher said Wednesday morning that speculation he will be tapped to serve as lieutenant governor is media-generated and his plans are to seek a second term in his Senate seat.