Several Democrats are considering a primary challenge to New York Gov. Andrew Cuomo, who plans to run for a third term next year.

Mr. Cuomo has a formidable campaign account of about $25 million and the advantages of incumbency, including alliances with labor unions and political committees. He has strained relations, however, with some liberal advocates, who see an opening for an insurgent on the left.

A Siena College poll in July showed a tie at 46% between voters who want him re-elected and those who don’t; among Democrats, however, 61% favor his re-election.

“In the last few years there’s been an earthquake in American politics, and Andrew Cuomo could well be surprised,” said Zephyr Teachout, the associate Fordham University law professor who lost a primary to Mr. Cuomo in 2014, but garnered a higher-than-expected 34% of the vote.

“Governor Cuomo has the strongest progressive record of any elected official in this country—period—and we look forward to building on that record in the third term,” said Bill Mulrow, his 2018 campaign chairman.


Here are three Democrats in the mix.

Syracuse Mayor Stephanie Miner

An outspoken critic of Mr. Cuomo’s, Ms. Miner will be term limited out of her mayoral job at the end of this year. She likely would focus her platform on infrastructure, a longtime priority of hers that has gained wider attention amid New York City’s public-transit woes.

“There are people reaching out to me,” she said. “If there was satisfaction with the job the governor is doing, then that wouldn’t be the case.”


Ms. Miner, 47, would need to increase her name recognition downstate but could be a serious opponent, analysts said. She also is considering a run for an upstate U.S. House Seat in 2018.

Former state legislator Terry Gipson

Mr. Gipson, 54, served one term as a state senator representing the Hudson Valley before losing to a Republican in 2014. He likely would run to Mr. Cuomo’s left.

“I’m talking to a lot of grass-roots organizations who want New York to be a leader in progressive legislation,” he said.


Mr. Gipson could rally liberals frustrated that Mr. Cuomo hasn’t fought harder to flip the state Senate to Democratic control, analysts said. But he would have a hard time catching up with the governor’s fundraising.

Actress Cynthia Nixon

The former “Sex & the City” star is being encouraged to run by liberal groups. Her candidacy has been floated before, but she shot it down in the past. Associates of hers said she is now considering it. She declined to comment.

Ms. Nixon, 51, has emerged as a liberal activist, campaigning in 2013 for New York City Mayor Bill de Blasio, and criticizing Cuomo policies on “The View” television show.


“She’s an out-of-the-box candidate with progressive credentials who would excite people,” said Billy Easton, director of the Alliance for Quality Education, a public-education advocacy group. While her candidacy would spark fanfare, it remains a long shot, analysts said.

Write to Mike Vilensky at mike.vilensky@dowjones.com