Hillary Clinton's next job? Surely not the one Mayor Bloomberg floated.

Hillary Rodham Clinton travels around the globe, negotiates with international leaders, and deals with the world’s crises. So, after she leaves her job as US secretary of State, as she has said she will next year, does she want to eat bagels and lox with the speaker of the City Council, mediate over the amount of sidewalk space a deli can use, and pat New York City sanitation workers on the back?

In short, does Mrs. Clinton want to run for mayor of New York in 2013?

As preposterous as that may sound, The New York Times reports that Mayor Michael Bloomberg, in his final year as “Hiz Honor,” has asked Clinton about succeeding him. Although the call took place several months ago – and Clinton has talked more of putting her feet up than of walking the city’s sidewalks looking for votes – it illustrates Mr. Bloomberg’s concern about finding a mayoral candidate with “star power” to succeed him.

"People are not always involved in picking their successor,” says Lee Miringoff, head of the Marist Institute for Public Opinion, in Poughkeepsie, N.Y. “It is unclear to what degree he was serious about reaching out.”

Political commentator Doug Muzzio wonders what Bloomberg might have been thinking. “Let me pick up the phone and call Hillary Clinton, since I’m not happy with the field” of candidates, says Mr. Muzzio, a professor at Baruch College in New York. “There is more than a little hubris here in picking your own successor.”

New York's last several mayors have tried to make the office into a national platform. Mayor Ed Koch called himself “mayor for life.” Rudolph Giuliani liked to think of himself as “America’s mayor.” And Bloomberg has used his three terms to highlight national problems such as obesity, global warming, and antismoking efforts.

True, being mayor of the Big Apple guarantees a certain amount of time on national television. When the ball comes down at Times Square on New Year’s Eve, the mayor is there. When the world watches the New York Marathon, the mayor is firing the starting gun.

"That is why Broadway is in New York City: The lights can shine on you and you can become a national figure,” says Mr. Miringoff.

So far, all of the announced candidates are local politicians. They include speaker of the City Council, Christine Quinn, and City Comptroller John Liu. Periodically, rumors float up that actor Alec Baldwin of “30 Rock” fame might dip his toes into politics.

But if Clinton were to show an interest in the job, often dubbed the “second hardest job in America,’’ the primary season would be short.

“If she decides to run, she clears the field,” says Muzzio. “She came within an eyelash of winning the Democratic nomination for president.”

But Clinton is very unlikely to run for mayor, he adds. “If she even remotely considers running, she should see a shrink,” he says. “She is not crazy; she is not going to do it.”

If Clinton were to run for mayor of the nation's largest city, she would need to move here. She and her husband, former President Bill Clinton, own a house in Chappaqua, N.Y., in Westchester County. To become mayor of New York, one must be among the 8 million residents of the Big Apple. Of course, that’s not difficult: She would just have to pay a few million dollars for a condo.

If such a transaction were to happen, however, don't read too much into it, Miringoff cautions. “It could just be for entertainment value,” he says. “If she’s interested in something down the road, it will have a Pennsylvania Avenue address, not a City Hall address.”