An upcoming book about Howard Stern by celebrity biographer Ian Halperin will include a bizarre claim that Frank Sinatra ordered a hit on the shock jock — but that goons may have murdered the wrong person by mistake.

The exposé, which Halperin is still writing, will claim that Ol’ Blue Eyes was furious because Stern went after his children in an on-air rant in the early 1990s.

“He criticized Frank Jr. and Nancy, and Frank lost his cool,” Halperin — who first revealed the tale on the “Anthony Cumia Show” podcast — told Page Six. “And everybody who ever knew Frank knew he was a nice guy, but you don’t want to piss him off. He had a big temper. And Frank ­allegedly put a hit on [Stern]. I have extreme corroboration on this.”

Halperin — who’s already written racy biographies on Michael Jackson, Brad Pitt and Angelina Jolie, and the Kardashians, among others — said his sources for the book believe an unnamed victim may have been accidentally whacked after being mistaken for Stern.

“A guy very similar to Howard’s profile — same height, same look, was killed in that era,” ­Halperin said.

Strangely, a similar claim was made in a book on Woody Allen that was released in October. Author David Evanier wrote in his tome, “Woody,” that Sinatra — whose ties to the mob have been chronicled ad nauseam — asked the Mafia to kill the director in retaliation for allegedly sexually abusing Dylan Farrow, Allen’s adopted daughter with Sinatra’s ex-wife, Mia Farrow. Allen has consistently denied any abuse claim.

“It’s going to be fair,” Halperin told us of the ­biography. “It’s not some hatchet job on Howard . . . I’ve no intention of doing that. Face it, he’s like 62 years old, he’s endured this long and he’s made the business better for everybody. But it’s going to be warts-and-all.”

Said a spokesperson for the Sinatra estate, “This is absolutely and completely ludicrous, and it’s someone using Frank Sinatra’s name to get their 15 minutes of fame.”