In a move that could open the door for a third term at City Hall, Mayor Bloomberg is staking out a new stance on term limits, saying he’d consider a bill to extend the time lawmakers can stay in office.

His openness to extending term limits via a City Council vote comes amid increased chatter in political circles that the mayor and the speaker of the City Council, Christine Quinn, are plotting to extend term limits to three terms from two.

After previously stating that he would respect the will of the voters on term limits, he refused yesterday to rule out supporting a term limits extension.

“If the City Council comes to us with a piece of legislation, we will look at it, we will consider it, and we will make what I hope is an informed judgment as to what is in the best interest of this city,” Mr. Bloomberg said. He later added: “The City Council has the legal right to change term limits.”

The statements indicate just how far Mr. Bloomberg has shifted his thinking on the subject in the past year. In December 2007, on the same day Ms. Quinn announced that she wouldn’t support any plans to change the term limit law, the mayor said he thought the council should be stripped of its ability to extend term limits.

“There is this technical imperfection, if you will, in the existing law that was approved by the public, where in theory the City Council could go and override the wishes of the public,” Mr. Bloomberg said at the time. “I think that should be taken away.”

New Yorkers voted twice in the 1990s in favor of limiting public officials from staying in office for more than two consecutive terms.

It appears that the business leaders eager to have Mr. Bloomberg stay in office for another four years are pushing him to re-examine his stance on the issue and entertain the possibility of trying to run for a third term. Despite Ms. Quinn’s previous promise not to touch term limits, support from the mayor for an extension could provide her with the political cover she would need to reverse her position. She has long been opposed to the city’s term limits law.

A spokeswoman for the speaker, Maria Alvarado, said yesterday that the mayor and Ms. Quinn had not had any conversations about term limits. When asked whether anyone on the council had requested that a term limits bill be drawn up or whether there was one in draft form, she declined to comment, saying that her earlier statement would have to suffice.

If the council does vote through an extension of term limits, the legislation could face a fight in court from the city’s leading champion of term limits, Ronald Lauder, who spent about $4 million on the term limits referendums in 1993 and 1996.

“Robbing the voters on term limits wouldn’t be easy,” a spokesman for Mr. Lauder, Nelson Warfield, wrote in an e-mail message. “Mr. Lauder considers all options on the table to defend term limits.”

Recently, however, Mr. Lauder has privately signaled that he wouldn’t fight an effort to extend term limits for the mayor by a referendum, according to a source with knowledge of Mr. Lauder’s conversations with business leaders on the subject. An effort to extend term limits through the council, without a direct say from voters, would be a different matter and could prompt him to take action.

Opponents of term limits argue that voters should decide at the ballot box whether they want more of the same representation or someone new, and complain that two terms doesn’t give elected officials in the city enough time to gain the experience necessary to be most effective. Thirty-six out of 51 council members are facing term limits next year.

A July poll by Quinnipiac University found that even though Mr. Bloomberg was the top pick among voters to be the city’s next mayor, 56% of voters said they are opposed to extending term limits to allow him to run for re-election.

Mr. Bloomberg, who said yesterday that he doesn’t have any plans to try to extend term limits and stay on, disputed the idea that his thinking on the matter has changed over time.

“You have previously asked me how I feel about term limits, and I have always said I think they have real advantages. I’ve tried in my company to change people around. I’ve tried in our administration to change people around,” he said. “Term limits are term limits. I am in favor of them. What’s an appropriate level? Whether it’s one term, two terms, three terms? I think you can debate that.”