Hillary Clinton (file photo)

Senator Clinton reportedly met with Mr. Obama in Chicago on Thursday.

But prior to a speech in New York on Friday, Clinton declined to say whether she was in the running to be the next secretary of state.

"Let me just say that I am not going to speculate or address anything about the president-elect's incoming administration, and I am going to respect his process and any inquiries should be directed to his transition team," she said.

Clinton and Obama were bitter rivals during the Democratic presidential primaries earlier this year. Some Clinton supporters were disappointed that Obama did not pick her as his vice presidential running mate, choosing Senator Joe Biden of Delaware instead.

Some Clinton associates like the idea of her becoming secretary of state. "She is an exceptional person, a great listener, someone who can look at the world through other people's perspectives," said former Clinton White House aide Lanny Davis on the Early Show on CBS television. "I think she has made a great U.S. senator for that reason, and I'm sure would make a great secretary of state for that reason."

Clinton's name has now been added to a speculative list of names for secretary of state that includes Massachusetts Senator John Kerry and New Mexico Governor Bill Richardson, both Democrats.

Republican Senator Richard Lugar of Indiana has also been mentioned, as has former Republican Senator Chuck Hagel of Nebraska.

Political experts note that, so far, few details have leaked out about which individuals are being considered for various jobs in the new administration.

William Galston worked in the Clinton administration and is now at the Brookings Institution in Washington. He's also a guest on VOA's Encounter program.

"We know very little because the transition team has been very discreet, and what was said of the [former President Ronald] Reagan transition, I think, is true of this one - those who know aren't talking, and those who are talking don't know," said Galston.

Meanwhile, the Obama transition team said the president-elect will meet Monday with his former Republican opponent, Senator John McCain of Arizona.

Experts do not expect Obama to offer McCain a job in the new administration, but they could talk over various areas of potential cooperation, once the new administration takes over in January.

"They will probably talk about the future, how Barack Obama can incorporate John McCain into his plans for governing," said Marc Ambinder, a political consultant for CBS News and an editor at the Atlantic magazine. "Remember, John McCain's core identity is that of a maverick and a reformer, someone who crosses party lines."

The Obama transition team is expected to announce more White House staff and Cabinet nominees in the coming weeks.

Barack Obama will be inaugurated as the 44th president of the United States on the steps of the U.S. Capitol building on January 20.