ARTHUR Miller, who never speaks publicly about his ex-wife Marilyn Monroe, has written a new play about her.

Called “Finishing the Picture,” it’s loosely based on the making of Monroe’s last movie, “The Misfits,” which Miller wrote.

A handful of Miller’s friends and associates, including David Richenthal, who produced the Tony Award-winning revival of “Death of Salesman,” attended a reading of the play last week.

“Arthur wanted to see how it works in front of an audience,” said one person who attended the reading. “It’s not a complete play yet. It really is just a draft.”

The Monroe character, called Kitty, is never seen but is constantly talked about by all on the set.

Kitty is having a nervous breakdown and is holed up in her hotel room, strung out on pills and booze. The other characters are trying to figure out how to get her back to work.

Some of the characters are based on the real people involved in the making of “The Misfits.”

In the reading, Harris Yulin played a character modeled on John Huston, who directed the movie.

Sam Robards played Miller’s alter-ego, a screenwriter who has recently broken up with Kitty.

Brian Dennehy read the part of a trucking company executive, who, through a corporate merger, has acquired the studio making the movie.

His character is said to be based on Steve Ross, who transformed his family’s funeral parlor business into Time Warner.

Frank Langella and Tovah Feldshuh played characters modeled on Lee and Anna Strasberg, the husband-and-wife acting gurus who had enormous influence over Monroe.

Both actors were said to be especially good in the roles. Langella was “pompous” and “creepy,” one source says, and Feldshuh “hilarious” as Kitty’s pushy acting coach constantly demanding limos and better hotel rooms.

“Arthur must have hated the Strasbergs,” one source says. “He really rakes them over the coals.”

Miller wrote another play about Monroe – “After the Fall” in 1964 – which many have seen as an attempt to exorcise his obsession with her.

But those who saw the reading of “Finishing the Picture” say it’s clear the great playwright is still, after all these years, grappling with it.

“This is a play about obsession, about how you give power over yourself to someone you are obsessed with,” one person says.

Another says, bluntly, “It’s about the beautiful woman who says she wants the sensitive and intellectual guy, but in the end always goes for the guy who treats her like s – – t.”

No word yet on when or where the play will be produced.

For a detailed and harrowing portrait of Miller’s relationship with Monroe, be on the lookout for Martin Gottfried‘s excellent biography of the playwright, “Arthur Miller: His Life and Work,” which will be published in September by Da Capo Press.

Gottfried, the former Post critic, devotes a chapter to the making of “The Misfits,” and it closely resembles Miller’s play.

“Seven weeks into the 10-week production schedule, [Monroe] was all but falling apart,” he writes. “Her emotional state had become precarious, her barbiturate dependency dangerous. At times, she was almost incoherent.”

At night, in their hotel room, Miller “could only watch as she swallowed her pills and, if she became anxious, keep her company through the night, carefully avoiding, he said, anything that might irritate her.”

Gottfried’s unauthorized bio, which has plenty of good theater gossip, also reveals Miller and his last wife, the late Inga Morath, had a son, Daniel, born with Down syndrome.

“He isn’t right,” Miller said of his son to the producer Robert Whitehead, describing the boy as a “mongoloid.”

“I’m going to have to put the baby away,” he added.

Daniel was put in a institution in Roxbury, Conn., and Miller never visited him, Gottfried reports.

The book is also notable for its incisive critical studies of Miller’s plays, and Gottfried makes a strong case for a relatively unknown masterpiece – the stage version of “Playing for Time,” which Miller adapted from his 1979 television movie about the women’s orchestra in Auschwitz.

Gottfried calls it Miller’s “most emotional play since ‘Death of a Salesman.’ “