Disgraced media mogul Les Moonves is threatening to sue CBS over recent leaks of lurid details about his alleged sexual misconduct, The Post has learned.

In what’s expected to amount to a breach of contract suit, Moonves’ lawyers are preparing to allege that leaks to the New York Times this week about CBS’ pending investigation into Moonves broke a confidentiality agreement and sullied the exec’s reputation, sources close to Moonves said.

At stake is a $120 million exit package for Moonves, which could get slashed or wiped out entirely if the board finds that CBS’ ex-chairman and chief executive violated the company’s harassment policies.

“He was about to get nothing,” an insider said of Moonves, citing the report’s damaging findings, including that the media exec had oral sex with at least four employees, as well as one network employee “on call” to pleasure him, according to a Wednesday report by the Times.

The 59-page draft report also claimed that Moonves destroyed evidence of his misdeeds and evaded investigators, and that CBS employees and some former board members covered up Moonves’ behavior.

With those confidential findings now public, lawyers for Moonves, who has said he believed the sexual encounters were consensual, believe they’ve now got a foot in the door to “challenge the process legally,” the source said.

“They think [the leak is] the dumbest thing they’ve ever seen,” the source said of Moonves’ lawyers, who have speculated that the report got leaked by somebody who “acted out of emotion” — either because of strong convictions about #MeToo issues or loyalty to Shari Redstone, the controlling shareholder and nemesis of Moonves.

The draft report was assembled by a pair of white-shoe law firms, Covington & Burling and Debevoise & Plimpton, that were hired in September, to conduct the Moonves investigation.

The identity of the leaker isn’t known, but sources close to the situation noted that Covington & Burling has offices are in the same building as the New York Times in Midtown Manhattan.

Indeed, Covington’s lawyers on the probe recently moved their Moonves-related meetings to another location, sources said. The firm did not return requests for comment.

The probe was nearing an end and it is believed that the board was ready to render a verdict in time for its annual meeting next Tuesday. But the report leaked to the Times “has thrown everything into chaos,” according to a source close to the situation.

Tom Johnson, a spokesman for the two firms conducting the probe, didn’t comment on the origin of the leak but sought to clear the board of any potential wrongdoing.

“No findings have been reported to the board,” Johnson said. “No draft of the investigators’ ongoing work product has been shared with the board or the company … Anyone who may have disclosed draft information to the New York Times did so without authority and in violation of their obligations.”

Moonves’ lawyer Andrew Levander declined to comment.

Dan Eaton, a partner at law firm Seltzer Caplan McMahon & Vitek who focuses on severance issues, speculates that the leak could only have come from the law firms at the behest of either CBS, a board member or Redstone.

“CBS is in a high-profile business. The viewing public cares about what the network’s officials do and why they do it,” Eaton said. “In this # MeToo moment, leaking the report may have been designed to boost the network’s case in the court of public opinion even as it may end up complicating the network’s case in a court of law.”

That brings back the question of the $120 million payout.

“If it’s zero, it’s game on,” said Eaton. “Moonves has 120 million reasons to sue. CBS is not going to give him anything more than zero unless he signs a release promising not to sue.”

According to Sam P. Israel, managing partner of his namesake Manhattan law firm, the leak was likely “calculated” and it gives CBS a good “negotiating position” in the case of a settlement.

Israel said the leak is a “message to the Moonves lawyer” that there’s evidence linked to a plethora of new claims.

“Moonves will probably get a settlement in the 10s of millions, not the $120 million,” Israel offered.

CBS declined to comment.