The decision settles one of the most discussed questions around his potential mayoralty. And it caps months of deliberations and a lobbying campaign by powerful New Yorkers pressing him to keep Ms. Tisch, a widely respected technocrat.

Choosing a leader for the 50,000-person department is among the most consequential decisions any mayor can make. But for Mr. Mamdani, a 34-year-old assemblyman with a history of caustic criticism of the police and ambitious plans to build a new community safety agency to take over some police functions, it could be unusually significant.

The two campaign officials, who were not authorized to speak publicly, said Mr. Mamdani viewed Ms. Tisch, 44, as a highly effective change agent who had overseen declining crime rates and cleaned up a department rife with allegations of corruption.

They also said that Mr. Mamdani felt confident he could work with her to implement key campaign promises, including creating the community safety department to shift responsibility for mental health episodes away from the police. Some police leaders have questioned the practicality of such an effort.

Mr. Mamdani has faced deep skepticism from police union leaders and withering campaign trail attacks from former Gov. Andrew M. Cuomo, his chief rival, portraying him as hostile to law enforcement and soft on crime.

Embracing a figure like Ms. Tisch before Election Day could help the Democrat address both potential vulnerabilities -- and send a clear signal that he is serious about building an administration staffed by experts who need not agree with him ideologically.

In this case, the differences are stark. He is a democratic socialist who once called the department "racist" and "anti-queer" and supported defunding it. (He has since disavowed those positions.) Ms. Tisch is a billionaire heiress appointed by Mayor Eric Adams who has pushed for stricter criminal justice laws.

Jeffrey Lerner, a spokesman for Mr. Mamdani, declined to comment or confirm the decision.

But Patrick Gaspard, an adviser briefed on the decision, said that the move reflected Mr. Mamdani's pledge to prioritize "excellence in every appointment that he makes" rather than any outside pressure.

He added that Ms. Tisch "certainly has demonstrated her excellence in the public role and in direct conversations."

Mr. Mamdani was likely to be asked about his plans again as soon as Wednesday evening during the final televised debate before the Nov. 4 election.

Ms. Tisch's allies have signaled for months that she would want to stay in the job regardless of the election's outcome. The campaign officials declined to detail any conversations between the candidate and the commissioner, but said they were confident she would accept.

Delaney Kempner, a spokeswoman for Ms. Tisch, referred a reporter back to an earlier statement from the commissioner stressing that "it is not appropriate for the police commissioner to be directly involved or to seem to be involved in electoral politics."

Mr. Mamdani's intention to offer Ms. Tisch the post comes as his campaign engages in broader deliberations over whether to publicly roll out personnel plans when Mr. Mamdani is leading in the polls but has yet to secure victory.

Mayors typically wait to announce any high-level hires until after Election Day. Breaking that tradition could leave Mr. Mamdani open to accusations that he is overconfident about the election and to second-guessing of his choices -- especially, in this case, among his far-left base that has opposed some of Ms. Tisch's policing strategies.

But Mr. Mamdani has also been under pressure to be more forthcoming given his age and relative lack of experience. And Mr. Cuomo has also said he would also ask Ms. Tisch to stay on if he gets to City Hall.

Mr. Mamdani and a team of aides plotting for a potential transition have been informally vetting candidates for first deputy mayor. Among those said to be under consideration for that job are Dan Garodnick, the city's planning commission chair; Maria Torres-Springer, who served as Mr. Adams's first deputy mayor; and a pair of Mayor Bill de Blasio's top deputies, Dean Fuleihan and Anthony Shorris.

For the critical police commissioner appointment, Mr. Mamdani appears to be following Mr. de Blasio's playbook. After running an election campaign criticizing the department's use of stop-and-frisk, Mr. de Blasio asked William J. Bratton, a respected former commissioner under Rudolph W. Giuliani, to return to the job.

In that case, the veneer of confidence instilled by the pick quickly wore off. Mr. de Blasio angered police officers after he invoked his biracial son, Dante, and said that for "so many of our young people, there's a fear" of the police. And when two police officers were killed at the end of Mr. de Blasio's first year, officers turned their backs to him when he appeared at their funerals.

Mr. Mamdani appeared to be preemptively taking steps to try to reassure his progressive base about his choice to retain Ms. Tisch.

Julia Salazar, a democratic socialist state senator who was briefed by Mr. Mamdani on the plan to keep Ms. Tisch, said in a statement that she trusted his decision. The commissioner's record of bringing down crime and overtime use, combined with the creation of the new agency, could be "a meaningful, positive shift in what policing looks like in our city," she said.

Ms. Tisch, whose family fortune is worth $10 billion, has a reputation for competence and ambition. She joined the Police Department's counterterrorism bureau in 2008 and helped build an app that provided officers with real-time information about emergency calls directly on their iPhones.

Mr. Adams, a former police captain and political moderate, initially appointed Ms. Tisch to lead the city's Sanitation Department, where she oversaw a trash containerization plan that finally standardized the use of plastic trash bins. He tapped her to lead the Police Department last November.

Business leaders, Gov. Kathy Hochul and Letitia James, the New York attorney general, have all lauded Ms. Tisch as commissioner.

As a candidate, Mr. Mamdani has distanced himself from many of the positions he took in summer 2020, as the city was convulsing in protests prompted by the police killing of George Floyd in Minneapolis. He has sought to meet with officers and police union leaders. He no longer wants to reduce the department head count, and has begun apologizing for past statements that he said were unfair and no longer reflected his views.

But he also intends to follow through on plans that are likely to face opposition within the department. In addition to creating the new community safety agency, he also wants to cut the Police Department's huge overtime budget and disband a unit known as the Strategic Response Group that handles protests.

Mr. Bratton said in a podcast interview released Tuesday that he would advise Ms. Tisch to turn Mr. Mamdani down should he ask her to stay.

"I think she would have an extraordinarily difficult time working with him if he is elected," he said. "Based on everything I've read about his positions, many of them are totally contradictory to hers. And you can't have that level of disagreement and be successful."

For Curtis Sliwa, the heat is on.