Mr. Boren declined to say which candidate would be strongest, but suggested “some kind of combination of those three: Bloomberg-Hagel, Bloomberg-Nunn.” He said Mr. Bloomberg would “not have to spend a lot of time raising money and he would not have to make deals with special interest groups to raise money.”

“Normally I don’t think an independent candidacy would have a chance” said Mr. Boren, who is the University of Oklahoma’s president. “I don’t think these are normal times.”

Mr. Bloomberg, who has tried to seize a national platform on gun control, the environment and other issues, has been regularly briefed in recent months on foreign policy by, among others, Henry A. Kissinger, his friend and the former secretary of state, and Nancy Soderberg, an ambassador to the United Nations in the Clinton administration.

Advisers have said Mr. Bloomberg, a billionaire many times over, might invest as much as $1 billion of his own fortune (he spent about $160 million on his two mayoral races) on a presidential campaign.

But they warned that while they were confident of getting on the ballot in every state, the process was complicated and fraught with legal challenges, and that Mr. Bloomberg would begin with an organizational disadvantage, competing against rivals who have been campaigning full time for years.

Still, the mayor said this month at a news conference, “Last I looked  and I’m not a candidate  but last time I checked reading about the Constitution, the Electoral College has nothing to do with parties, has absolutely nothing to do with parties. It’s most states are winners take all. The popular vote assigns electoral votes to the candidate, and I don’t think it says in there that you have to be a member of one party or another.”

The key players  virtually the only players  in Mr. Bloomberg’s embryonic campaign are three of his deputy mayors, Kevin Sheekey, Edward Skyler and Patricia E. Harris. Another aide, Patrick Brennan, who was the political director of Mr. Bloomberg’s 2005 re-election campaign, resigned as commissioner of the city’s Community Assistance Unit earlier this year to spend more time exploring the mayor’s possible national campaign.