The NYPD may or may not be the greatest police department in the world, but it does have the greatest number of rumormongers.

Take the retirement this week of Chief of Department Carlos Gomez, the NYPD’s highest-ranking uniformed officer and its highest-ranking Hispanic cop.

Foremost among the rumors — more certainty than rumors — is that Gomez’s successor will be Chief of Patrol Terence Monahan. He is pals with Commissioner James O’Neill, who promoted him to chief of patrol in 2016. Monahan is a hard-nosed commander and no stranger to controversy. As a deputy chief, he directed police operations at the Republican National Convention in 2004, when 1,806 people were arrested, and many were held for three days. When the Civilian Complaint Review Board sought to question him about the arrests, then-Commissioner Ray Kelly refused to allow him to be interviewed.

So who’s Monahan’s successor as chief of patrol? Rumors are that it’s Assistant Chief Rodney Harrison, who as Monahan’s executive assistant heads the mayor’s neighborhood policing program. Harrison is black, which is both a rarity and an asset in the NYPD’s three-star ranks.

Rumor also has it that certain powerful females outside the department — for example, Public Advocate Letitia James and Mayor Bill de Blasio’s wife, Chirlane McCray — would like to see a woman, primarily a woman of color, in a high and visible position. That could mean Queens North Assistant Chief Juanita Holmes.

Then, there’s the impending departure of Chief of Detectives Bob Boyce, who ages out at 63 in a couple of months.

Rumored to succeed him is Dermot Shea, the chief of crime control strategies. He’s so dedicated, he supposedly sleeps in his office every Wednesday night, poring over pages of crime data to prepare for the next day’s CompStat meeting with department brass.

Missing from the rumors are Hispanic officers. With Gomez’s departure, there are none above the two-star rank of assistant chief, which in the NYPD ranks higher than deputy chief. And there are only a few Hispanic assistant chiefs.

With Hispanic cops comprising about 30 percent of the force, that’s something the NYPD will have to reckon with.