Former Secretary of State Condoleezza Rice has no interest in running for Senate, according to a senior adviser, removing a big name from California Republicans' recruitment list as they hope to compete for retiring Sen. Barbara BoxerBarbara Levy BoxerBottom line Trump administration halting imports of cotton, tomatoes from Uighur region of China Biden inaugural committee to refund former senator's donation due to foreign agent status MORE's (D-Calif.) seat.

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"It's not even a consideration," Georgia Godfrey, Rice's chief of staff, tells The Hill via email. "She's happy here at Stanford!"

Republicans began bandying around Rice's name as a dream candidate shortly after Boxer announced her retirement plans Thursday morning. But Rice, who's working as a professor at Stanford and a Hoover Institute fellow, has shown no interest in running for office either in California or nationally over the years despite topping GOP wish lists for a number of races. She's also rumored to be a candidate to run the University of Texas system.

Rice isn't the first Republican to remove her name from consideration. Sources close to Rep. Darrell Issa (R-Calif.) told The Hill earlier on Thursday that he has no interest in a run.

Republicans nationally and in California privately admit that it's unlikely they'll be able to mount a serious challenge for Boxer's seat, while Democrats are bracing for what could be a crowded and expensive primary campaign with a number of potential top-tier candidates.