Bush national security adviser Condoleezza Rice, looking ahead to her political future, has "talked specifically" to high-level GOP insiders about the possibility of running for California governor in four years -- and has ruled out a 2004 U.S. Senate campaign against Democratic incumbent Barbara Boxer, Republican Party sources said.

Rice, the former Stanford provost who rates highly with California voters in opinion polls, is "very much open" to a future gubernatorial run in the nation's most populous state, according to those high-level Republicans.

Though they admitted much depends on the outcome of the expected U.S. war in Iraq, Republicans at the state's recent party convention openly speculated that a Rice campaign could instantly recharge a party still reeling from losses in every statewide office this past November.

"She's said no on the Senate race, but is very much open on '06," said a Republican insider who asked not to be identified. The Republican said Rice sees herself as more compatible with an executive position such as governor than a legislative office.

Mark Baldassare, pollster for the Public Policy Institute of California, said Rice is "a very visible figure in the Bush administration, very articulate, has roots at Stanford -- and would be taken very seriously."

"In a state where you have to look long and hard for elected officials outside the white male category on the Republican side, Condi Rice would certainly add a new dimension to GOP politics in California," Baldassare said. "It would help (Republicans) deal with what is becoming a stereotype -- that they don't have women and people of color."

While preliminary polls show Rice's name recognition and positive ratings are high in California, her political future is heavily tied to the outcome in Iraq -- where she has strongly advocated the use of military force.

"It really depends on the war . . and that's a big if," says Democratic political consultant Gale Kaufman of Rice's potential as a candidate. "She's completely wrapped her arms around Iraq -- and I'm not sure that's as good a resonating message here as it would be somewhere else."

Said one leading GOP strategist who spoke not for attribution: "Depending on what happens (on the national front), she could be strengthened or hurt -- and even then, Bush still has this thing called the economy."

Rice's office declined comment on the discussion of her political prospects.

With two years before the next statewide campaigns, some Republicans have already skipped past that, instead salivating at the scenario of a GOP "battle of the titans" in the 2006 Republican primary for governor -- should actor Arnold Schwarzenegger, also widely speculated to be interested, and Rice join the campaign.

Some GOP insiders were pushing Rice to consider a Senate bid against Boxer next year and accomplish double duty -- winning a seat held by Democrats since 1992 and improving President Bush's chances to take California.

Republicans who have expressed interest in the Senate contest include former gubernatorial candidate Bill Simon and Reps. Doug Ose of Sacramento, Darrell Issa of Vista (San Diego County), and George Radanovich of Mariposa.

GOP sources say Rice has specifically raised the 2006 gubernatorial run with top administration officials, though they caution that any move is far down the road and the president's re-election campaign is the top political priority.

Still, a party source said Rice would "have to consider it fairly soon after the '04 election. She's expressed a willingness to consider, not to close the door."

The ambitions expressed by Rice -- who once said she dreamed about becoming the commissioner of the National Football League -- aren't surprising given her history, political observers said.

"I'm sure she aspires to political office because all of her moves have really led her in that direction," said Barbara O'Connor, professor of political communications at California State University at Sacramento. "She's smart and she's got management experience, certainly as much as anybody who runs for governor. Being (Stanford) provost is like running a large corporation -- and she's been tested and vetted in high circles."

But O'Connor said Rice still would face challenges in Democrat-leaning California. Some voters "may find her a bit strident and . . . be concerned about her really conservative leanings," she said. "In California, that hasn't proven to be an attractive set of values" for a candidate.

And there's already political day-dreaming about how she would do in a primary battle against Schwarzenegger. That would almost certainly pose headaches for the Democrats, but would excite California voters -- a sharp contrast to the 2002 election, in which voter turnout sank to record lows, with people expressing disgust with the major candidates.

"Talk about a bipolar election. It would be the most interesting thing in the world to watch," O'Connor said. "You couldn't have two more dissimilar people -- and it would provide voters with a great choice."