It seems unlikely — but the idea’s been floating around for several days now, and so far she’s not rejecting it. For what it’s worth, Secretary Clinton, we’d love to see you run for mayor. New York City needs you.

Yes, we were highly critical of Hillary Clinton in the runup to Election Day. But that was the race for the White House, where she offered a program far to the left of the nation’s center.

Not so in New York, where she’d be dead-center in the city’s Democratic majority. Progressive, but not obsessed with proving it — nor with trying to use the mayoralty to become a national leader. Passionate for social justice, but not an ideologue who’ll stick by homeless or affordable-housing policies that are clearly failing.

Above all else, she’d actually focus on doing the job. Clinton is a famously diligent worker — one who shows up on time and puts in the hours. And New York needs a mayor who’ll run herd on city government.

The incumbent has handed the work of running the city off to one or two deputies, while he spends his time on politics and p.r. stunts. And it shows — in the details those overworked deputies let slip, like that Rivington Street nursing-home flip, and in the crises that go too long unacknowledged, from the Bronx outbreak of Legionnaire’s disease to the surge in street homelessness.

Clinton is a fighter and a problem-solver. For eight years, she was a fine senator for this state, working relentlessly on 9/11 recovery and also for constituents in areas far from the media spotlight.

Sure, she’d need to become a city resident, and spend months building ties to Gotham’s neighborhoods. But she’s hardly a stranger to the city, nor it to her.

Nor does any local Democrat seem both willing and able to seriously challenge Mayor de Blasio for reelection — yet he needs to be challenged, indeed needs to be replaced.

Plus, her national stature would bring serious benefits: She’d be a lot harder for Gov. Cuomo to bully than the current mayor — and tougher for Washington to ignore.

Nor would she need to sell herself to the city’s special interests to win the job — another huge improvement over the incumbent.

What’s in it for her? Well, her presidential run shows her appetite for continued public service. And while Gracie Mansion isn’t the White House, it’s no consolation prize: New York’s mayor is famously “the second-toughest job in America” — and you traditionally have your own foreign policy, too.

While it’s not the glass ceiling she hoped to break, New York has never had a woman mayor. Isn’t it past time for that to change?