E.T. phone Broadway?

Oscar-winner Steven Spielberg could soon be directing a stage show — his first — here in New York, sources told The Post.

A new musical put on by the Public Theater, the mysterious work is said to be currently being written by Jeanine Tesori and Tony Kushner.

I hope it’s “Jaws!”.

The acclaimed trio makes for a high-brow Venn diagram of collaborators.

Kushner, the celebrated “Angels in America” playwright, penned the Spielberg films “Munich,” “Lincoln,” “West Side Story” and “The Fabelmans” — all Best Picture Oscar nominees (though just one hit).

And, combining forces with “Kimberly Akimbo” composer Tesori, Kushner wrote the book and co-wrote the lyrics of the 2003 musical “Caroline, Or Change.” She was also the supervising vocal producer on Spielberg’s “West Side.”

Details of their new project are scant. Tesori has dealt with a complicated and secretive family before in Best Musical Tony winner “Fun Home.” Maybe this will be “The Fabelmans — On Ice!”.

Or “Disclosure Day!” featuring a line of tap-dancing aliens shuffling off to Jupiter.

I gather — and if Spielberg and Kushner’s screen collabs are any indication — it’s more “Caroline” than “Saving Private Ryan.”

The Post has reached out to the Public for comment.

What is known is that the show is meant to be timed to outgoing Public artistic director Oskar Eustis’ farewell, and would open sometime in 2027-2028, his final season. 

Sixty-eight-year-old Eustis, who recently told the New York Times, “I think the American nonprofit theater movement is over,” clearly wants to greet the apocalypse with a bang. 

During his 21 years in the top job, his theater’s shows “Hamilton,” “Hell’s Kitchen,” “Here Lies Love,” “Suffs” and plenty more have made the leap to Broadway — one much more successfully than the others. He used to get flack for his apparent obsession with it. Spielberg’s show also surely would transfer uptown, too.

How could they resist? This would be the extremely rare circumstance where the director’s name alone has the potential to sell some tickets. But you never know. When major pop stars write musicals, for example, their involvement doesn’t always budge the box office. Only quality and buzz do.

Strangely, famous filmmakers giving the stage a go is a growing trend.

Historically it flowed in the opposite direction: theater folk headed to Hollywood. Think playwright and director Martin McDonagh, whose Oscar hopeful “Wild Horse Nine” hits theaters this weekend. Sam Mendes, Mike Nichols, Bob Fosse and Orson Welles are others.

But it was recently announced that cinephile favorite Quentin Tarantino will also make his theater directing debut next February in London with a new swashbucking play he’s written called “The Poppinjay Cavalier” starring Sacha Baron Cohen. Sadly, it’s not “Inglourious Bastards: A Musical Fable.”

The Public would actually make an easy commute for 79-year-old Spielberg. Earlier this year, he and wife Kate Capshaw moved from LA to Manhattan. And his Amblin Entertainment opened an office in New York.

And there have been hints of Spielberg’s love of musicals sprinkled throughout his storied career. Obviously, there was the film adaptation of “West Side Story.” But nerds will also recall he also had “Indiana Jones and the Temple of Doom” open with a Mandarin-language rendition of “Anything Goes.” 

Nevertheless it’s a risky move. Spielberg is renowned for his genius at moving around a camera. Visually, every one of his films is a wonder. But in the theater, we’re the camera. And we sit still until intermission. It’s a totally different skill. 

But I sure look forward to Tesori’s uptempo ballad “It’s A Dinosaur!” from “Jurassic Park the Musical.”