James E. McGreevey, a former New Jersey governor who resigned two decades ago in scandal, has built his career on reinvention. So much so that when he enters a classroom filled with newly freed felons hoping to make the most of their own second chance, they are not sure what to call him.

“Governor!” the instructor bellows.

“Jim — come on, guys — it’s just Jim!” he counters affably as he fist-bumps several men enrolled in a post-prison career training program he founded and now leads as executive director.

Mr. McGreevey, 66, has tried on other titles since he quit politics in 2004 after announcing to his second wife and to the world that he was gay and had had an affair with a man who worked for him.

He published a book, “The Confession,” and starred in a documentary produced by Alexandra Pelosi, a daughter of the former House speaker. He earned a master’s degree in divinity. He had hoped to be ordained an Episcopal priest, but amid the fallout of his bitter divorce the church turned him down.

And now Mr. McGreevey, a Democrat who once was thought to have the White House in his sights, is making plans to do what he had said he would not: re-enter politics.

Over the past several months, Mr. McGreevey has begun cobbling together support for an expected run for mayor of Jersey City, the state’s second-largest city, where he has lived for eight years.

Minutes from New York and teeming with progressive newcomers, Jersey City enjoys a prominent place in regional lore, filled with immigrants, innovation and working-class brio. But it is also 63 miles away from the State House and its attendant power and trappings.

Mr. McGreevey, who was born in Jersey City, says he has no problem with the perceived downgrade in prestige.

“Being governor is so much about the budget, the dollar,” he reasoned during an interview at the job training center in Kearny, N.J., run by his current employer, the New Jersey Reentry Corporation. “Being mayor is about building strong communities.”

He added, “It’s also a worthy place to put my energies, to hopefully do some good.”

He expects to make a final decision before Thanksgiving.

“I’m getting closer to making that decision in the affirmative,” he said.

At least three other Jersey City Democratic leaders are also seriously considering vying for the job. The current mayor, Steven Fulop, who is running for governor, does not intend to run for re-election. But the contest is not until November 2025, setting up a two-year runway in which anything might happen.

“I could be dead by then,” said Gerald McCann, 73, a former Jersey City mayor now advising Mr. McGreevey.

Still, few would dispute that Mr. McGreevey is winning the race for buzz and institutional support among key power brokers in Hudson County.

Nine of the county’s 12 mayors have publicly endorsed his candidacy. A recent fund-raiser for a nonprofit civic organization named for his parents, who, he stressed, were raised in Jersey City, drew labor leaders and local and state officials. And on Saturday he is convening the first of what he calls “listening sessions.”

On a recent morning, he wandered the halls of the training center with the confidence of a school principal and the lively gait of a St. Patrick’s Day parade grand marshal. He was eager to discuss the state-funded program in minute detail, including the 268,402 pounds of food it has provided this year to clients, the role of the on-site chaplain and the facility’s free medical and dental services.

His phone rang during the interview, and he answered it cheerfully. It was a young detainee at a state psychiatric facility who had been assigned to him as part of the client caseload he maintains, even as executive director. He listened patiently and asked if the man had read the book he shared, “Band of Brothers.”

It is his work with current and former prisoners and the insight it has offered about their lack of educational and workplace preparedness, and the realities of the impoverished communities they return home to, that most guides his current ambition, he said.

“My sense is Jersey City is at a tipping point, and it ought to be affordable for those families that have lived in the city for three or four generations,” he said.

Fans of Mr. McGreevey’s candidacy cite his decades of government experience. Before being elected governor, he was an assemblyman, state senator and mayor of Woodbridge, a sprawling suburban township in central New Jersey.

Mr. McGreevey’s 21-year-old daughter, Jacqueline, who, with her older half sister, Morag, grew up in the shadow of their father’s spectacular crash-landing from politics, said part of her wishes he would remain out of the limelight.

“I genuinely think that he would do a lot of good for a lot of people,” she said between classes at Barnard College, “so it feels kind of selfish to not want him to pursue it.”

“My dad always says, ‘Do the next right thing,’ ” she said, “whether it means study for the next test or help the next person.”

“This seems to be kind of a natural progression of where he’s been,” she added, “and what he wants to do.”

Whatever happens, Mr. McGreevey said he does not see the job as a steppingstone.

“I’m walking down the hill,” he said. “This is it.”

Jersey City’s mayoral elections are nonpartisan, a detail that diminishes the ability of county political bosses to design the ballot to all but guarantee a win for their handpicked candidates, as occurs in many other places in New Jersey.

Mr. Fulop, who did not have the backing of the county Democratic Party when he was first elected mayor, has not commented on Mr. McGreevey’s potential candidacy. The two have a fraught history: Mr. McGreevey was fired from a job in Jersey City in 2019 after Mr. Fulop and his aides suggested the former governor had misallocated funds, a claim Mr. McGreevey said was untrue and was disproved by independent audits.

The mayor of Union City, N.J., a powerful county leader, was first to champion Mr. McGreevey’s candidacy, generating a cascade of early institutional support.

But two possible Democratic opponents, William O’Dea, a county commissioner, and James Solomon, a city councilman, argued that this outside support, while helpful for fund-raising, could also backfire.

“It’s creating this overarching question: ‘Why are these folks who have nothing to do with our city imposing their will on our city?’ ” said Mr. O’Dea, who also held a political fund-raiser this week.

Mr. Solomon said voters were savvy enough to think for themselves.

“I haven’t met a voter in Jersey City who is concerned with the opinions of power brokers outside of Jersey City,” Mr. Solomon said. “They’re concerned about rents going through the roof and political cronies stealing their tax dollars. They’re going to vote for the candidate who can make their life better.”

Politics is not the only community Mr. McGreevey has returned to.

After years as an Episcopalian, he has rejoined the Roman Catholic Church, unable to walk away for good from the faith that shaped him as a child and younger man.

He attends Mass regularly at Christ the King, a predominantly African American congregation in Jersey City, parishioners say. He is friendly and contributes to the upkeep of the parish. His homosexuality, which the catechism of the Catholic church does not approve of, is not an issue, they say.

“We accept him. He accepts us,” said Ann Warren, 63, the parish business administrator.

Still, in a city where more than 75 percent of residents are nonwhite, Ms. Warren said the concerted push by county leaders to “recycle their buddies” and put him at the front of the line smacks of the “hypocrisy of the Democratic Party.”

Joyce E. Watterman, the first Black woman to serve as City Council president in Jersey City, is among the three likely mayoral candidates pushed to the side as Mr. McGreevey was elevated.

“It’s like, ‘We’re all for minorities and blah, blah, blah,” said Ms. Warren, a lifelong resident of Jersey City.

“But we’re not willing to invest the funds to put them in positions that matter. It’s just the same old boy network.”