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 BoxerFeinstein to hold campaign fundraisers, a hint she'll run again Becerra formally nominated for Calif. attorney general 10 freshmen to watch in the new Congress 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.