With more than two-thirds of the 51-member City Council facing term limits in 2009, a new wave of leaders is coming under scrutiny at City Hall as speculation begins to stir over who may be the next council speaker.

Council members Daniel Garodnick of East Midtown and the Upper East Side, Inez Dickens of Harlem, and Maria del Carmen Arroyo of the South Bronx are being viewed as potential successors to Speaker Christine Quinn by political observers, council members, and aides.

Assemblyman Herman “Denny” Farrell, who is eyeing the seat of a council member of West Harlem and Washington Heights, Robert Jackson, also is considered a contender for the post.

“Do the job you got before you do the job you want,” Mr. Farrell, the chairman of the state Democratic Party between 2001 and 2006, said when asked if he would seek the speaker’s seat if elected to the council.

Mr. Farrell would be the first first-term speaker since the position was created. Council members and others have said they don’t believe Mr. Farrell, who is up for re-election in 2008, would leave Albany unless he was positioning himself for the top leadership position.

Mr. Garodnick and Ms. Arroyo demurred when asked if they are trying to become the next speaker, saying they are focused on doing their jobs. Ms. Dickens, however, said she would be interested in the position.

“In ’09, there are only going to be about 13 or 15 of us left,” Ms. Dickens, who heads the council’s standards and ethics committee, said. “There are many of us that may be interested in it.”

Ms. Arroyo, chairwoman of the aging committee, said, “It’s a little too early to even begin having discussions about that kind of stuff.” Mr. Garodnick, chairman of the planning, dispositions, and concessions subcommittee, said selecting a new speaker “is an issue that is years away.”

The next speaker of the council, considered the second most powerful elected position in the city, will be elected by the council in January 2010, but the real decision making often takes place outside City Hall.

“The election of the speaker is less about the peers choosing you and more about the county leaders wheeling and dealing,” the executive director of the government watchdog Citizens Union, Dick Dadey, said. “When the public vote occurs it’s nearly unanimous because the behind the scenes vote has already taken place.”

The position was created in 1990, after the city’s charter was rewritten, giving new power to the council.

A move to the council would likely mean a pay raise for Mr. Farrell, who earns $79,500 as an Assemblyman and an additional $34,000 for his chairmanship of the powerful Ways and Means Committee. The base salary for council members is $112,500, with the speaker earning an additional $28,500. Even if Mr. Farrell did not become the next speaker, his pay would almost surely rise with a committee chairmanship or leadership position, which brings in thousands of dollars in additional pay.

A professor of public policy at Baruch College, Douglas Muzzio, said it is too early to think about who will replace Ms. Quinn, especially since there will be so many new members elected in 2009.

“That’s the wild card,” he said. “Thirty-six other people who could be speaker, and those people we don’t even know yet.”