Can You Imagine Bill de Blasio as Governor? He Can.

Mayor Bill de Blasio has begun to tell people privately that he plans to run for governor of New York next year, according to three people with direct knowledge of his conversations with fellow Democrats and donors.

Mr. de Blasio, who has been a polarizing figure during his two terms in office, has also sounded out trusted former aides about their interest in working on a potential campaign, according to two people who are familiar with those contacts, and has made other overtures to labor leaders about a possible bid. His longtime pollster conducted a private survey to assess Mr. de Blasio’s appeal beyond New York City. And publicly, too, he has increasingly made it clear that he wants to remain in public life.

“There’s a number of things I want to keep working on in this city, in this state,” Mr. de Blasio said last week, noting his interest in public health, early childhood education and combating income inequality. “That is going to be what I focus on when this mission is over. So, I want to serve. I’m going to figure out the right way to serve and the right time to serve.”

Mr. de Blasio’s move toward a possible run for governor comes even as the city he now leads faces extraordinary challenges and an uncertain future, and should he enter what may be a crowded and well-financed field, he would face significant hurdles.

His approval ratings in New York City have been low, according to the sparse polling that is publicly available, and he faces deep skepticism elsewhere in the state — an environment similar to the one he confronted, unsuccessfully, in his 2020 presidential bid. A run for governor would be contrary to the better judgment of even some people he considers allies, as well as that of many party leaders across the state.

“Osama bin Laden is probably more popular in Suffolk County than Bill de Blasio,” said Rich Schaffer, the chairman of the county’s Democratic committee, who endorsed Gov. Kathy Hochul on Monday. “De Blasio, I would say, would have zero support if not negative out here.”

At a debate during New York City’s Democratic mayoral primary this year, the candidates were asked to raise their hands if they would accept Mr. de Blasio’s endorsement. Only one contender did so — a sign of the mayor’s standing in his own party.

He could also face significant competition in the city, let alone the rest of the state. New York’s attorney general, Letitia James, who, like Mr. de Blasio, is from Brooklyn, is thought to be nearing a final decision concerning a possible campaign. Jumaane D. Williams, another Brooklyn Democrat and the city’s public advocate, has already begun exploring a potential run, and others in the party are also weighing whether to get into the race.

Asked whether New York should have another white male governor — Ms. Hochul is the first woman to lead the state; Ms. James and Mr. Williams are Black, and Ms. James could be the first Black woman to govern any state in the country — Mr. de Blasio appeared to brush aside the question last week.

“We need people of all backgrounds to be involved in government,” he said.

His plans could change. Peter Ragone, the adviser who may be closest to Mr. de Blasio’s deliberations, insisted that the mayor had not made a determination.

“The simple fact is that he hasn’t made any final decisions at all about what he’s doing next,” Mr. Ragone said. “The mayor believes in public service because he can do things like push universal pre-K and 3-K. That’s why millions of New Yorkers have voted for him in the past 12 years, to the dismay of political insiders.”

Many New York Democrats are incredulous that Mr. de Blasio would run and, simultaneously, believe that he may do so, pointing to his failed presidential bid as proof that he has an appetite for challenging campaigns and a steadfast belief in his own political potential.

Marc Molinaro, the Dutchess County executive and unsuccessful candidate for governor in 2018, said that many of his fellow Republicans, as well as independent voters around the state, blame Mr. de Blasio for the “rise in crime and the deterioration of the economic and social strength of New York City.”

Even so, Mr. Molinaro, who said he gets along well with Mr. de Blasio, warned that it would be unwise to discount the mayor’s political prowess.

“I would not underestimate his ability to develop a coalition within his party,” Mr. Molinaro said. “He’s very skilled at that.”

Mr. de Blasio’s allies, too, note that in his mayoral runs, he assembled a diverse coalition in the nation’s largest city, with strong support from Black voters, although that dynamic is hardly guaranteed to transfer to a potentially crowded field in a statewide race.

The Rev. Al Sharpton, the civil rights leader, said that he had spoken with Mr. de Blasio about a potential run recently but that the mayor had not indicated whether he had reached a final decision.

“He has some standing in the progressive community, he has some standing in communities of color,” Mr. Sharpton said. “He should not be taken lightly.”

Other veterans of New York politics were less interested in discussing the mayor’s future prospects.

“I very seldom pass, but I don’t want to get involved in anything that would be negative,” said Charles B. Rangel, the former congressman from Harlem, after laughing when asked for his thoughts on a potential run by Mr. de Blasio. “And I cannot think of anything positive.”