The city’s leading champion of term limits is privately signaling a new openness to a third term for Mayor Bloomberg.

Several business leaders who have spoken with businessman and philanthropist Ronald Lauder have left with the impression that he would not challenge an effort to extend term limits by a referendum, a source with knowledge of the conversations said.

A private indication by Mr. Lauder that he would sit on the sidelines during an effort to extend term limits could embolden opponents of the law and those who are eager to see Mr. Bloomberg run for re-election.

The current law bars elected officials from running for a third, consecutive term and will force the mayor from office at the end of 2009.

Although Mr. Bloomberg has said publicly that he would abide by the will of the city’s voters and uphold the city’s term limit laws, business leaders are urging him to change them so that term limits are extended for all citywide offices and for the City Council, a source close to City Hall said.

When the source appealed to the mayor to extend term limits, Mr. Bloomberg responded that he was “thinking about it,” the source said.

“He’s said he’s been thinking about it for quite a while now, but he’s a realist. He won’t do something that will damage his legacy if he doesn’t think the public will go for it,” the source said.

A recent Quinnipiac University poll highlights the quandary facing the mayor as he wrestles with the term limits question. When New York City voters were asked last month about whom they’d like as their next mayor, Mr. Bloomberg was the top pick, but a majority of voters, 56%, said they oppose extending term limits to allow him to run for re-election.

A spokesman for Mr. Lauder, Nelson Warfield, said anyone trying to tinker with term limits would face resistance from Mr. Lauder.

“These un-named business leaders should leave impressions to comedians. They are totally off-base,” Mr. Warfield wrote in an e-mail message yesterday. “Mr. Lauder will defend the voters’ choice of a two-term limit for city politicians as-is. And the in-depth polling we have done shows voters won’t tolerate any tinkering with the law. Do these people really think voters want to reward the distinguished public servants who gave us the City Council slush fund scandal with more time in office?”

In April, it was disclosed that the council had been stashing million of dollars behind fictitious organizations in its budget each year.

Kathryn Wylde, the president of a business organization, the Partnership for New York City, said Mr. Lauder’s colleagues in the business community hope that he would not oppose an extension of term limits to 12 years, because she said the 8-year limit has produced a churning in government that is not serving the public interest.

Term limits were introduced in the city in 1993 and approved by voters in a second referendum in 1996 after Mr. Lauder, the son of cosmetics magnate Estée Lauder, spent about $4 million on the two citywide campaigns.

In 2009, 36 members of the City Council will be term-limited out of office. Many of them are running for other political offices, which include the positions of mayor, city comptroller, public advocate, and the borough presidents. Ms. Wylde said that most elected officials “hardly learn their job before they are forced to start looking for a new one.”

New Yorkers who want to extend term limits would have to begin acting soon. The window is closing fast for filing a petition to place an amendment to the city’s term limit law on the November ballot. After September 5, there will be no way to change the law by petition this year.

It appears that even if the required signatures were collected and turned in to the city today, it still would be difficult to place the measure on the ballot because of time constraints laid out in the law.

Other options for extending term limits would be for the mayor’s charter revision commission, which he is expected to appoint before leaving office, to propose changing the law. Such a change would have to be approved by voters, but it could be done in a special election. The council also could act on its own to amend term limits, although Speaker Christine Quinn has said she would not do that.

When asked about overturning term limits at a press conference in Brooklyn yesterday, the mayor said: “It’s not going to take place.”

“It’s a hypothetical question,” he said. “I can only say this: I love the job. I’ve got 514 days left and there will be plenty of things for me to do after this.”