Yes, they met -- but Clinton as madame secretary of state?

Advisers confirmed on Friday that President-elect Barack Obama had met with Sen. Hillary Rodham Clinton on Thursday evening at Obama's transition office in Chicago to discuss what role Clinton might play in his administration.

Their private session stoked speculation that she was being considered for secretary of state, perhaps the most prestigious Cabinet position, but associates of both Democrats cautioned that their conversation was mostly general and that no job was offered. However, one Democratic official -- while cautioning that Obama had given no indication that he was leaning toward her -- said Obama asked Clinton directly whether she would be interested in the job.

Where she stands for the post came into question as Democrats said another primary rival, Bill Richardson, was brought in as well. Obama met with the governor of New Mexico in Chicago on Friday, a day after his one-on-one with Clinton.

Still, the fact that Obama and Clinton had even met to discuss such a possibility left even some of their closest advisers buzzing about the pros and cons of so close a partnership, and about how it would be complicated by a third wheel -- former President Bill Clinton.

Obama was out of sight Friday. Clinton addressed a conference in New York and said, "I'm not going to speculate or address anything about the president-elect's incoming administration, and I'm going to respect his process."

The two are not the only candidates Obama has talked to others about the job. Some believed to be under consideration include Sen. John Kerry, D-Mass., retiring Sen. Chuck Hagel, R-Neb., and Wisconsin Gov. Jim Doyle, who was contacted Friday by the transition team, a gubernatorial spokesman said.

Obama was deciding on his presidential staff as well, naming longtime friend and mentor Valerie Jarrett as a White House senior adviser. The official announcement is expected today. It is one of the key early assignments of the Obama administration and comes on the heels of speculation that Jarrett might serve as head of a federal agency.

Obama also reached out to his Republican opponent, John McCain, inviting him to meet on Monday.

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 and a ban on torture. 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 power. Republican Sen. Lindsey Graham, a McCain confidant, and Rahm Emanuel, whom Obama has chosen to be his White House chief of staff, also plan to attend the meeting.

Would Clinton be interested?

Choosing Clinton would be a striking decision for Obama. The possibility of Clinton joining Obama in such a role has been bandied about in Washington for several months, usually with the caveat that it was somewhere between unlikely and far-fetched.

But on Thursday Clinton was spied boarding a plane to Chicago -- on "personal business," a spokesman said -- and by early evening a small motorcade of black SUVs emerged from the garage of the Chicago building where Obama has his transition office, just minutes before Obama's own motorcade left. Clinton, as a former First Lady, travels in a government SUV.

Should he pick her, Obama might further unite and energize his party, make clear to the world that he is serious about diplomacy and send a substantive political signal to women.

And, unlike the vice presidency that Obama never seriously considered her for, as secretary of state she would serve at his pleasure.

That said, there are clear dangers for Obama as well, not least of them any lingering rivalry between the two. He would also inevitably be sharing the stage with both Clintons, with all of the baggage that accompanies them. Moreover, now that Obama's consideration of Clinton has become public, he faces another danger: the risk of reopening old wounds in the party and among Democratic women in particular if he does not appoint her to a top job.

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 staying in the Senate may not be her first choice, either, because she is a junior senator without prospects for a leadership position any time soon. She approached Senate Majority Leader Harry Reid about becoming chairman of a special subcommittee to handle health care issues, but he squelched the idea, officials said.

"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.

The Associated Press, Chicago Tribune and McClatchy News Service contributed to this report.