Lisa Monaco during her Senate Select Intelligence confirmation hearing to be assistant attorney general for national security at the Department of Justice. (Scott J. Ferrell/Congressional Quarterly)

The Obama administration has begun to search for a replacement for FBI Director Robert S. Mueller III, and for the first time one of the leading contenders is a woman.

One of several people under consideration, according to current and past administration officials, is Lisa Monaco, who left a senior post at the Justice Department this month to become President Obama’s top counterterrorism adviser.

Mueller, 68, will step down Sept. 4 after 12 years on the job. Since taking the helm a week before the Sept. 11, 2001, attacks, Mueller has overseen the bureau’s transformation into a worldwide counterterrorism operation.

The director’s job is limited to 10 years by law, but the Senate in 2011 extended Mueller’s term for two years at the request of President Obama after a search for a replacement failed.

Officials said the administration wants to find a successor soon so that person can be vetted, nominated and confirmed before Congress goes on summer recess. In the early stages, the process is being coordinated by the Justice Department.

“Mueller will leave very big shoes to fill,” said one Justice Department official, who spoke on the condition of anonymity because he was not authorized to speak to the press. “Two years ago, he was portrayed as the indispensable man. Now, the FBI is going to have to do without the indispensable man in a matter of a few months.”

Among the names that have surfaced as contenders are Monaco, who oversaw the National Security Division at Justice before moving to the White House; Merrick B. Garland, chief judge of the U.S. Court of Appeals for the D.C. Circuit; James B. Comey, deputy attorney general in the George W. Bush administration; Neil MacBride, U.S. attorney for the Eastern District of Virginia; and Patrick J. Fitzgerald, former U.S. attorney in Chicago.

Spokeswomen for the White House and the Justice Department declined to comment on the search. Other current officials described the process on condition that they not be identified when talking about internal deliberations.

“The problem we quickly ran into two years ago is that there just aren’t a lot of people who have Bob Mueller’s stature, but eventually you have to face the fact that he can’t stay in the job forever,” said Matthew Miller, a former Justice spokesman. “No one can fill his shoes on day one, but we’re four years into the administration now, and there are a number of talented people who have added some significant experience to their résumés.”

The next FBI director will lead an agency with a more complex and demanding mission than the agency Mueller took before the Sept. 11 attacks. Since then, he has led the bureau’s evolution from traditional crime fighting to a heavy focus on preventing terrorist attacks.

While Mueller has won bipartisan support through two administrations, the bureau has increased its surveillance operations in ways that critics say sometimes violate civil liberties.

Law enforcement experts said that the new director will need to be experienced in both law enforcement and management, given the vast expansion of the FBI’s operations over the past decade.

Monaco, 44, would be the first woman to lead the FBI. Before heading the National Security Division at Justice, she was a counsel to former attorney general Janet Reno, an assistant U.S. attorney for the District of Columbia and Mueller’s chief of staff at the FBI.

One concern about Monaco mentioned by department insiders is that she just became Obama’s chief counterterrorism adviser, replacing John Brennan when he became CIA director.

“The president is going to be personally relying on her to fulfill that role,” said one Justice official. “They might not be open to having a revolving door in that critical position at the White House.”

But another administration official said Monaco’s move to the White House might work in her favor because the president can closely observe her leadership skills.

Other contenders have pluses and minuses. Garland and Comey, both of whom were considered two years ago, are highly respected and experienced, but there are questions about whether either would want the job.

Fitzgerald, regarded as an independent-minded prosecutor, might face a tough confirmation because he prosecuted and convicted I. Lewis “Scooter” Libby, former vice president Dick Cheney’s top aide, in the Valerie Plame leak case. MacBride has established a strong track record for prosecuting national security cases, a mainstay of the bureau’s operations.

Konrad Motyka, president of the FBI Agents Association, which represents more than 12,000 active and retired agents, said several possible candidates have contacted him for advice and support. Motyka declined to name anyone, but he said he will be discussing them with members of Congress and administration officials in the coming weeks.

Jim Pasco, national executive director of the Fraternal Order of Police, which represents more than 325,000 officers, said that the next FBI director needs to possess a deep understanding of law enforcement. Pasco suggested that the White House consider a veteran police official, such as Philadelphia Police Commissioner Charles H. Ramsey or New York City Police Commissioner Raymond W. Kelly.

“The FBI is a huge bureaucracy, so the director has to be someone who can manage, first and foremost,” Pasco said. “To his credit, Bob Mueller has done a yeoman’s job in trying very hard to reach out and work with other agencies. But there is a continuing gap in the relationship the FBI has with state and local law enforcement and other federal agencies.”