If the field of 2009 mayoral candidates were limited to the four leading contenders, the speaker of the City Council, Christine Quinn, would be the most likely to win an endorsement from Mayor Bloomberg, political observers say.

Mr. Bloomberg recently said that he has his own views about who will replace him; since then, speculation about which candidate he favors has gained added steam.

Ms. Quinn has worked in lockstep with the mayor on policy issues, including campaign finance reform and an overhaul of the city’s building code, and is considered the candidate most likely to carry out his long-term goals for the city.

“She has worked with him so closely, and the council has generally worked with the mayor on major issues,” a Democratic political consultant, George Arzt, said. “She is very close to this administration.”

Mr. Arzt said that gives Ms. Quinn the biggest edge in winning a mayoral endorsement over the other candidates, who include Rep. Anthony Weiner, the president of the Bronx, Adolfo Carrion Jr., and the city’s comptroller, William Thompson Jr.

The head of New York Civic and a former parks commissioner, Henry Stern, also said the mayor would probably prefer Ms. Quinn to the other three leading Democrats, but noted that there will almost certainly be more candidates seeking the seat as the election date draws nearer.

The race, he said, is “by no means” limited to those four candidates. “I mean who was he before he ran?” Mr. Stern said, referring to Mr. Bloomberg. “He basically came from outer space.”

Mr. Stern also noted that Ms. Quinn’s cooperation is crucial to the mayor’s agenda, and that by holding back on publicly naming his preferred successor, Mr. Bloomberg has more leverage to push his agenda through the council.

“She’s like Silver and Bruno rolled into one,” Mr. Stern said, referring to Assemblyman Sheldon Silver and state Senator Joseph Bruno, the powerful leaders of the Legislature in Albany.

The president of the Partnership for New York City, Kathryn Wylde, would not speculate about whom Mr. Bloomberg would endorse, but said she is certain Mr. Bloomberg wants someone who will carry out his long-term initiatives.

Ms. Quinn’s relationship with Mr. Bloomberg, a hallmark of her term as speaker, was highlighted in front of a national audience on Monday night during a TV interview with Charlie Rose, who said Ms. Quinn seemed to be a great admirer of the mayor.

At first, she downplayed her relationship with Mr. Bloomberg, characterizing it as an essential part of doing her job.

“I have to get stuff done, so I don’t have any choice but to get along and work with the mayor,” Ms. Quinn said. “I mean fighting with the mayor won’t help New Yorkers.”

She later heaped on the praise, saying Mr. Bloomberg is a “great politician” who is focused on problem solving, finding answers, and “getting the job done.”

Mr. Bloomberg, who left the Republican Party in June, is believed to be contemplating a bid for the White House, even though he has said he is not running. During the interview on PBS’s “The Charlie Rose Show,” Ms. Quinn said that she supports Senator Clinton for president and expects her to win. Many political observers have said, however, that if the city’s police commissioner, Raymond Kelly, Deputy Mayor Daniel Doctoroff, or a business executive such as the CEO of Time Warner, Richard Parsons, joined the candidate pool, Mr. Bloomberg would likely back one of them.

Mr. Arzt said Mr. Bloomberg’s endorsement will carry a lot of weight and is something every candidate will want. When asked whether Ms. Quinn could be elected mayor without Mr. Bloomberg’s support, Mr. Arzt said, “Let’s put it this way, it would be much easier with.”

A political consultant for Ms. Quinn, Mark Guma, would not say whether the speaker has sought an endorsement from Mr. Bloomberg. “Right now, she is focused on being speaker,” he said.

Not everyone keeping tabs on the mayor’s race thinks Ms. Quinn is in a position to gain Mr. Bloomberg’s official support. Some observers, including political consultant Hank Sheinkopf, said it’s not clear whom Mr. Bloomberg will endorse. Mr. Sheinkopf said the relationship between Ms. Quinn and the mayor reveals nothing about what will happen down the line.

“The alleged closeness today does not necessarily follow into an endorsement two years down the road,” he said.

The director of the Marist Institute for Public Opinion, Lee Miringoff, said that even if Mr. Bloomberg does not endorse Ms. Quinn, he could be expected to at least say nice things about her during the campaign.

“He wants someone who will carry on or at least credit his legacy,” he said. “Clearly, there has been a good working relationship.”