After all, the gossip column called the news “a wild rumor flying around the TV industry” and published it on April Fools’ Day.

Others, like Monica Klein, a political consultant who once worked for Mayor de Blasio, saw it as another reminder that the city has never elected a woman to its top office. In contrast, yesterday Chicago elected Lori Lightfoot as mayor, becoming the largest American city to ever choose a black woman as its top official.

In New York, Mr. Zucker joined a list of men who have been named as potential 2021 mayoral candidates: City Comptroller Scott Stringer, City Council Speaker Corey Johnson, Bronx Borough President Ruben Diaz Jr. and Brooklyn Borough President Eric Adams.

(Letitia James, the former city public advocate, was thought to be a promising candidate before she became the state attorney general.)

The question in New York “isn’t so much who could run and win as a woman, but what does the fact that we only have an all-male field tell us about the lack of developing female leadership in this city?” Ms. Klein said.