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(CNN) -- President-elect Barack Obama met with his former rival Sen. Hillary Clinton to see if she would be interested in a role in his administration, two sources told CNN Friday.

Obama also will meet with the man he defeated in the general election, Republican Sen. John McCain, on Monday, the Obama transition team announced Friday.

On Friday, Clinton responded to the latest rumors at a transit policy speech in Albany, New York.

"I'm very happy there is so much press attention and interest in transit," Clinton said to laughs.

"In the off chance that you're not here for this important issue and are here for some other reason, let me just say that I'm not going to speculate or address anything about the president-elect's incoming administration."

She added: "I'm going to respect his process and any inquiries should be directed to his transition team."

Clinton went to the meeting Thursday with Obama because "she knew Obama wanted to talk about whether she would have a role in the administration," one of the sources knowledgeable about the meeting said.

Obama and Clinton met in Chicago, Illinois, at the request of the president-elect, the sources told CNN.

The two sources said Clinton was surprised to hear rumors she was being considered for secretary of state position. The sources could not confirm that the she and Obama discussed the nation's top diplomatic position or that it was offered.

This is not the first time Clinton has been rumored to be under consideration for a position on Obama's team.

The New York senator was said to be on Obama's short list of possible vice presidential picks this summer, but Obama ended up picking Sen. Joe Biden of Delaware.

That source said Clinton thought the speculation that she would be tapped to be Obama's secretary of state was "silly" because of the earlier buzz about her becoming Obama's running mate. iReport.com: Who should Obama pick?

A spokesman for the former presidential candidate and first lady, Philippe Reines, said "any speculation about Cabinet or other administration appointments is really for President-elect Obama's transition team to address."

On Monday night, while walking into an awards ceremony in New York, Clinton was asked if she would consider taking a post in the Obama administration.

"I am happy being a senator from New York. I love this state and this city," she said. "I am looking at the long list of things I have to catch up on and do.

"But I want to be a good partner and I want to do everything I can to make sure his agenda is going to be successful." Watch whether Clinton would join Obama's team »

Other names that have been mentioned for the top diplomatic role include Sen. John Kerry of Massachusetts, the Democrats presidential nominee in 2004, and New Mexico Gov. Bill Richardson, a former U.S. ambassador to the U.N. and energy secretary in the Clinton administration.

Latino groups are championing Richardson for the top State Department slot. If picked, Richardson would be the nation's first Latino secretary of state.

A source close to transition team tells CNN that Obama is also trying to build a diverse Cabinet that includes women and minorities and that works as a team.

Obama's transition team is expected to announce some high-level staff positions on Friday.

Obama campaign spokesman Robert Gibbs is widely expected to be named White House press secretary, and Obama chief strategist David Axelrod is expected to be picked as a White House senior adviser.

After Michelle Obama crossed the threshold of her new home yesterday to meet with its outgoing occupants, she was briefed on what would convey: certain pieces of furniture, the carpeting and the drapes -- if these met her tastes -- and, of course, a tremendous sense of history. Meeting privately with Laura Bush while her husband conferred with the president in the Oval Office, the incoming first lady was participating in a century-old Washington ritual that represents the softer side of the serious business of a presidential transition.

It's a tradition that may not rank with the passing of secret nuclear-launch codes, but the White House visit by Michelle and Barack Obama was no less freighted with significance. "They will literally become living symbols of the country to the world, for all of history," said Carl Sferrazza Anthony, who has written several books about first ladies. "It will redefine their identities."

Michelle Obama had already made clear that her first priority will be smoothly settling her daughters, Malia, 10, and Sasha, 7, into this new life. She squeezed the White House visit in between trips to the private Georgetown Day School and Sidwell Friends School.

The transition team and staff at both schools in the District refused to discuss the visits. So it fell to a 10-year-old boy, Nicolo Pisoni, to offer on-the-record confirmation of her trip to Georgetown Day's campus on MacArthur Boulevard.
 

"I thought it was awesome because I saw the future first lady," the fourth-grader said. "I got really excited, but we weren't supposed to get excited. Not out loud. Our teachers told us not to get excited but to show Michelle it was a regular school day and that we aren't crazy kids. They didn't want us asking her for her autograph."

Isabel Dorval, a 10th-grader at Sidwell, said she was running on the field at the middle/upper school campus on Wisconsin Avenue a little after 4 p.m. when a convoy of cars arrived. About 45 minutes later, the motorcade drove off as Sidwell students waved. Michelle Obama rolled down the window and waved back: "It was cool," said 15-year-old Isabel.

Past presidents have sent their children to both public and private schools. But sources familiar with the process say they expect the Obamas to select a private school, where tuition for both girls would total more than $50,000 a year. The girls attend a private school now near their Chicago home, and Michelle is on the board of trustees.

As is customary during transitions, the outgoing first lady led her successor on a White House tour that focused primarily on the upstairs private residence, including three bedroom suites and three living areas. These areas, along with the Oval Office, are subject to redecoration, as opposed to the public rooms. A stop on the tour always of particular interest, Anthony said, is the first lady's sitting room, whose windows afford a direct view of the Oval Office below: "She can really keep an eye on who's coming and going, who's meeting with the president."

Michelle Obama and Laura Bush also spent time discussing "raising daughters in the White House," Stephanie Cutter, the Obama transition spokeswoman, said in a statement. "Mrs. Obama was honored to finally meet the First Lady, who was a gracious hostess." It was Michelle's second visit to the White House -- she was there once before with Malia and Sasha around the time of her husband's swearing-in to the Senate.

On MSNBC, Anita McBride, Laura Bush's chief of staff, said the first lady showed Michelle Obama where the Bush daughters, Jenna and Barbara, lived.

"She thought the rooms were beautiful and would be perfect for her two little girls and that they could decorate in a way that would be appropriate for young children," McBride said. "And it is a historic room. The Kennedy children lived there. The Johnson girls lived there, Chelsea Clinton as well . . . and Amy Carter."