Not even a year into New York City mayor’s first term, Eric Adams’s plummeting popularity is inspiring his political foes to consider challenging him in the next mayoral race.

The first challenger to step out of the shadows may well be from stage-right. Greg Kelly, the son of a former New York City police commissioner, has teased his interest in running against the mayor on Twitter and his radio show.

Mr. Kelly, a former Marine and Fox News correspondent, would be the first candidate to enter the race against Mr. Adams.

Six months into his term, Mr. Adams’s approval ratings are already tanking. In a recent NY1 poll, fewer than a third of New Yorkers said the city was headed in the right direction — and more than half said it was headed in the wrong one.

As a red-meat Republican, Mr. Kelly would likely face an uphill climb to Gracie Mansion. The conservative is a supporter of President Trump and has claimed that the 2020 election was stolen.

While he hasn’t officially entered the race, Mr. Kelly seems to be modeling any potential candidacy around that of Mr. Trump’s.

Mr. Kelly wrote in a Trumpian tweet Tuesday night that “lots of people think” he should pursue the office of mayor. “But right now, I have ‘no plans’ to run.”

On his radio show Wednesday, Mr. Kelly was less coy, bashing Mayor Adams for traveling to Washington, D.C., to testify in favor of gun control instead of fighting gun violence at home. He again teed up the possibility of a challenge to the incumbent.

“I’m listening. I’m trying to see if anybody else is taking him on,” he told listeners. “Maybe I will.”

“My priority would be getting lunatics … off the street; getting the ‘woke’ crap out of the schools; bringing sanity, law, and order back to New York,” he added.

The former Marine pilot has criticized the mayor for being soft on crime. His military background could be an asset in a race against Mr. Adams, who ran as a tough ex-cop ready to clamp down on crime in the 2021 election.

If he ran, Mr. Kelly would likely have to address a rape allegation made against him in 2012. No charges were filed and the case was ultimately dropped, and Mr. Kelly returned to his job as the host of “Good Day New York” on Fox’s New York affiliate, WNYW.

The mayoral race would not be the first Kelly-Adams showdown. The Sun’s editorial pages once called Mr. Adams a “demagogic critic” of Mr. Kelly’s father, the former NYPD commissioner, Raymond Kelly.

In 2013, Mr. Adams testified against Commissioner Kelly in a high-profile federal lawsuit alleging that the department’s “stop and frisk” policy unfairly targeted black and Latino men solely because of their race. 

The elder Mr. Kelly was a named defendant in the case, along with Mayor Bloomberg.

In his testimony, Mr. Adams, then a state senator, accused Mr. Kelly of engineering stop-and-frisk specifically to scare black and Latino men. 

Mr. Kelly “stated that he targeted and focused on that group because he wanted to instill fear in them that every time that they left their homes they could be targeted by police,” Mr. Adams testified. “I told him that was illegal.”

The case was ultimately decided in favor of the plaintiffs.