The meeting with Clinton, revealed to The Associated Press Friday, excited a burst of speculation that Obama would transform the former first lady and his fierce campaign foe into one of his top Cabinet officials and the nation's chief diplomatic voice. But where she stands in contention for the post came into question as other Democrats, also speaking on condition of anonymity about the private discussions, said Richardson was brought in as well.
Obama was silent and out of sight in Chicago. New York Sen. Clinton addressed a transit conference in her home state and said emphatically, "I'm not going to speculate or address anything about the president-elect's incoming administration, and I'm going to respect his process."
Obama also is reaching out to Republican Sen. John McCain, hoping to make an ally of the man he defeated for the presidency only last week. Obama meets with McCain on Monday.
And he was making decisions on his presidential staff as well, naming longtime friend Valerie Jarrett as a White House senior adviser. Jarrett met Obama when she hired his wife for a job in the Chicago mayor's office years ago and has been a close confidante to the couple ever since.
Richardson is the governor of New Mexico and has an extensive foreign policy resume. He was President Bill Clinton's ambassador to the United Nations and has conducted freelance diplomacy for the U.S. in such hot spots as Sudan and North Korea.
Richardson also served in Clinton's Cabinet as energy secretary, and angered his former boss when he endorsed Obama after ending his own primary campaign this year.
Advisers to both McCain and Obama say they don't expect an administration post for the defeated Republican presidential nominee, but Obama's aides say he would like to have the Arizona senator partner with him on legislation they both have advocated, such as climate change, government reform, immigration and a ban on torture.
All this fits with an idea that Obama often talked about on the campaign trail, as he praised the presidency of Abraham Lincoln as described by Doris Kearns Goodwin in her book "Team of Rivals."
"Lincoln basically pulled in all the people who had been running against him into his Cabinet because whatever personal feelings there were, the issue was: How can we get this country through this time of crisis?" Obama said at one point.
Lincoln appointed three of his rivals for the Republican nomination to his Cabinet. Obama turned to one rival for vice president, picking Democratic primary candidate Joe Biden even though Biden had questioned whether Obama had the experience to be president.
In his first two weeks as president-elect, Obama has struck a bipartisan tone. He paired a Republican and a Democrat to meet with foreign leaders this weekend on his behalf in Washington, for example.
It's far from clear how interested Clinton would be in being his secretary of state. She'd face a Senate confirmation hearing that would certainly probe her husband's financial dealings - something the Clintons refused to disclose in the presidential campaign.
But remaining in the Senate may not be Clinton's first choice, either, since she is a junior senator without prospects for a leadership position or committee chairmanship any time soon.
Democratic officials, speaking only anonymously about private negotiations, say Clinton asked Sen. Edward Kennedy to establish a subcommittee that she would lead that would allow her to shepherd health care reform through the Senate. But Kennedy, chairman of the Senate Committee on Health, Education, Labor & Pensions, wants to lead the effort as a capstone to his career, and there also are other members with more seniority than Clinton whom he wouldn't want to bypass.
Being secretary of state could give Clinton a platform for another run at the presidency in eight years. Obama could also get assurances from her that she wouldn't challenge him in four years.
And, unlike the vice presidency that Obama never seriously considered her for, as secretary of state she would serve at his pleasure.
Clinton didn't give any clues to her thinking when she addressed a public transit industry conference Friday in Albany, N.Y., beginning with a joke about news accounts of her trip to Chicago.
"I'd like to start by saying I'm very happy there is so much press attention and interest in transit, especially questions about my own," she said. She ignored reporters trying to question her about a possible post as she left.
Another Democrat emerged as a possible contender for an administration post Friday - Wisconsin Gov. Jim Doyle was contacted by Obama's transition team, according to a gubernatorial spokesman who did not disclose details. Doyle, a two-term governor and former state attorney general, was an early backer of Obama.
An alliance between Obama in the White House and McCain in the Senate could help both sides - Obama by having a Republican ally on some issues, and McCain to help rebuild his own power. The two men spoke about getting together when McCain called Obama to concede on Election Night, advisers on both sides say.
Republican Sen. Lindsey Graham of South Carolina, a McCain confidant, and Rep. Rahm Emanuel, the Illinois Democrat whom Obama has chosen to be his White House chief of staff, also plan to be at Monday's meeting in Chicago.
"It's well known that they share an important belief that Americans want and deserve a more effective and efficient government, and will discuss ways to work together to make that a reality," Obama spokesman Stephanie Cutter said in announcing the meeting.
Associated Press writers David Espo, Jim Kuhnhenn and Liz Sidoti in Washington, Richard Richtmyer in Albany, N.Y., and Scott Bauer in Madison, Wis., contributed to this report.