A woman from “48 Hours” running “60 Minutes”? You must be joking.

Snooty correspondents at CBS’ “60 Minutes” are apoplectic over the idea that Susan Zirinsky — the longtime boss of the network’s crime-focused “48 Hours” news show — could soon be their boss.

The Post reported on Friday that 66-year-old Zirinsky had become the front-runner to succeed longtime “60 Minutes” executive producer Jeff Fager, who left the award-winning show last month amid accusations of inappropriate conduct and sexual harassment.

In response, top correspondents at “60 Minutes” over the weekend called members of CBS’ board to complain — with some threatening to resign if Zirinsky got the top job. One top correspondent even called Richard Parsons, who was interim chairman of CBS until Sunday, when he stepped down citing health reasons, according to a source.

While the identity of the miffed correspondents couldn’t be learned, one source noted that at least one was “approaching retirement age” and might have less to lose by threatening resignation.

A CBS spokeswoman declined comment on specifics of the race for Fager’s job, but added that “no decision has been made.”

Zirinsky has lately been in a neck-and-neck race with Fager’s longtime No. 2 exec, Bill Owens, according to sources close to the situation. But last week, insiders say CBS brass began leaning toward Zirinsky.

After the explosive allegations of sexual misconduct that toppled CBS boss Les Moonves last month, the CBS board has been searching for ways to signal that the network is making bold moves to change the company’s image as a boys club, insiders said.

Indeed, the appointment of Zirinsky as executive producer of “60 Minutes” — the first female and only the third to lead the 50-year-old series — could mark a wider succession plan at the show.

A source told The Post that “60 Minutes” senior producer Tanya Simon, the 47-year-old daughter of the late “60 Minutes” correspondent Bob Simon, could be named Zirinsky’s No. 2 and eventually succeed her.

Nevertheless, “60 Minutes” staffers are skeptical of Zirinsky’s track record at “48 Hours” — dominated by segments on serial killers, terrorists and school shootings. Meanwhile, however, one insider suggested that 51-year-old Owens, who has taken over Fager’s duties as the show’s interim executive producer, is liked by insiders mainly because longtime staffers “don’t like change.”

Since Fager’s departure, employees have been filing into the offices of CBS News president David Rhodes and EVP Ingrid Ciprian-Matthews, pleading that they promote Owens and ditch Zirinsky, according to sources.

“The major correspondents want Owens,” a source said.

In an effort to quell the troops, Zirinsky circulated a memo over the weekend, denying widespread reports that she is poised to move to “60 Minutes.”

Sources confirmed on Tuesday that Owens is still in the running alongside Zirinsky and that they are the top two internal candidates at CBS for the role. It isn’t clear whether recent employee protests could give him the edge, a source said.

One outside candidate who has been rumored for the job is Vice Media’s Josh Tyrangiel, but an insider with knowledge of the talks said Tyrangiel is “not even in the running.”

Despite his now-toxic reputation, former CEO Moonves “was the guardian angel of ‘60 Minutes,’ ” according to one source, adding, “There’s lots of fear. It looks like there’s no leader now. It looks like chaos.”