The Hill News

Count at least one prominent Arizona Republican out of the race to succeed Sen. Jon Kyl (R-Ariz.): Gov. Jan Brewer.

In a press statement Thursday evening, the Arizona Republican said she has no intention of running for Kyl’s seat when he retires in 2012.

“You can bet that I’ll be following the 2012 race closely, as it has serious ramifications for Arizona," Brewer said in the statement. "I will not, however, involve myself in this contest as a candidate. Arizona faces serious issues and needs a full-time governor, and I intend to see this state’s recovery to completion.”

Kyl said Thursday that he would not run again.

Brewer, a fierce critic of the Obama administration, had not indicated much interest in running for Senate any time soon, but likely could have been a solid Republican candidate because of her strong stances on illegal immigration and border security generally favored by the right.

On Thursday, ! Brewer announced a countersuit to the federal government in response to a controversial immigration law she signed last year. (Read the text of Brewer's countersuit here.)

Other names mentioned as possibilities in the race for Kyl's seat include former Rep. J.D. Hayworth (R-Ariz.), who challenged Sen. John McCain (R) last year, and Homeland Security Secretary Janet Napolitano, the Democratic governor of Arizona preceding Brewer.

Hayworth said he's considering running for Kyl's seat. Napolitano has not indicated whether she plans to run.