If Mayor Giuliani loses his bid for the White House, he could always turn around and run for mayor of New York.

The city’s term limit laws bar politicians from serving more than two consecutive terms in office, but wouldn’t prohibit Mr. Giuliani from trying to win back his old office at City Hall.

The race to replace Mayor Bloomberg in 2009 already is shaping up, but could take place even sooner if Mr. Bloomberg wins the presidency or resigns to campaign full time. In the event of a vacancy, the public advocate, Betsy Gotbaum, would become mayor, and a special election would be held on the first Tuesday that falls at least 60 days later, barring a few exceptions.

Mr. Bloomberg denies that he will run for president, but speculation that he will jump into the race is rampant.

In either case, Mr. Giuliani could find himself perched at the top of the Republican mayoral field, which has been quiet thus far with the emergence of only one likely candidate, a businessman, John Catsimatidis. Police Commissioner Raymond Kelly is often mentioned as a potential Republican candidate, but has denied plans to run. Another potential Republican candidate is the chairman and former chief executive of Time Warner, Richard Parsons. But if Mr. Bloomberg won the presidency, it’s likely that Mr. Parsons and Mr. Kelly would end up with jobs in Washington.

A political science professor at Fordham University who was a congressional fellow in Senator Clinton’s office between 2004 and 2005, Costas Panagopoulos, said Mr. Giuliani should run for mayor if he loses his bid for the White House, and predicted he’d do well in the race. He said he is not affiliated with Mrs. Clinton’s campaign.

Mr. Giuliani “seemed to have a passion for running the city of New York, and I suspect it might be something that is attractive to him and to voters in the city,” Mr. Panagopoulos said. “He has a strong chance of winning.”

He said it’s possible Mr. Giuliani would suffer from the same difficulties known to encumber elected officials who run for reelection after mounting a losing presidential campaign.

He said his research has found that unsuccessful presidential candidates who also were members of Congress or governors came in about 7% points lower when running for reelection than they did before campaigning for president. He studied candidates from the late 1940s through the early 1990s.

“We haven’t had lots of cases of former mayors running, so it’s hard to know if that pattern holds,” he said. “My sense is that there is some segment of the electorate that feels progressive ambition comes at the expense of local interest.”

The minority leader of the City Council, James Oddo, who is supporting Mr. Giuliani for president, said he’d want America’s mayor back at City Hall, but said such a move is unlikely.

“I think being mayor of the city of New York is kind of like law school. It’s painful when you go through it and you probably say to yourself, ‘I never want to do that again.’ But when you look back you say, ‘I’m glad that I did it,'” he said.

Mr. Oddo predicted Mr. Giuliani would win easily if he ran again for mayor, despite a perception among some, he said, that the former mayor couldn’t run for dogcatcher.

A Quinnipiac University poll from August indicates New Yorkers aren’t clamoring for Mr. Giuliani to return to his old post. They’d rather see Mr. Bloomberg stay in office for a third term.

When respondents were asked who they would like to see elected mayor in 2009, 3% said Mr. Giuliani and 21% said Mr. Bloomberg. Mr. Giuliani came in ahead of other potential mayoral candidates: the Speaker of the City Council, Christine Quinn, and Mr. Kelly, who were each named by 1% of those polled.

In October 2001, 79% of New Yorkers surveyed in a Quinnipiac poll said they approved of Mr. Giuliani, a boost from his 50% approval rating before the terrorist attacks on New York on September 11, 2001.

A professor at Cooper Union who is a historian of Mr. Giuliani’s administration, Fred Siegel, predicted that if the former mayor lost his presidential campaign, he’d be more inclined to launch another White House bid in 2012 before setting his sights on City Hall.

“He’s an international player. I don’t think he has any interest in worrying about sewage in Queens,” said Mr. Siegel, who supported Mr. Giuliani when he ran for mayor in 1993 and 1997 and is the author of “The Prince of the City,” a book about Mr. Giuliani.

He said the former mayor would be a divisive figure in a mayoral election, in part because he’d be returning to govern a city he has derided on the campaign trail as an unruly metropolis he had to tame.

“It’s just so far off the map,” he said. “I can’t imagine.”