What is it about some movies that make them ripe for remakes? Take A Star Is Born, currently going through its fourth interpretation, with Bradley Cooper and Lady Gaga in the starring roles.

The original was a 1937 tearjerker with Fredric March and Janet Gaynor. The second go-round, in 1954, was a musical starring Judy Garland and James Mason.

But perhaps the most intriguing (and controversial) adaptation was the 1976 film, staring Barbra Streisand — who co-produced the movie with her then-boyfriend Jon Peters and singer-songwriter Kris Kristofferson. But what some may not know is that Streisand’s first choice for the role of John Norman Howard was none other than Elvis Presley.

That’s right. The world’s greatest diva and The King almost appeared together in the now-famous story of a star on the skids who falls in love with an up-and-coming talent. According to those close to Presley, he wanted to do the movie. His movie career had stalled and his recording career was in a slump, with his last top ten single being Burning Love, three years earlier.

The two superstars met (at least) twice. The first time was when Streisand was performing at the International Hotel in Las Vegas. Elvis came to her show and afterward went backstage, surprising the singer in her dressing room.

A nervous Streisand was painting her fingernails so she didn’t have to look Presley in the face. In a commentary track for the DVD release of A Star Is Born, Streisand mentioned that Presley, incredibly, took the bottle of nail polish, got down on his knees, and started painting her nails.

They would meet up again in 1975 when Streisand and Peters came to Presley’s dressing room, after one of his Vegas shows, to pitch the part. Jerry Schilling, then a member of Presley’s entourage, “The Memphis Mafia,” and one of his closest friends, was present at the time.

In a 2002 interview, Schilling recalled that he was surprised to see Streisand because when he and Presley had gone backstage to her dressing room a few months earlier, and Streisand asked Presley what he thought of her show, he replied, “You’ve got a great voice Barbra, but you keep putting your hand in front of your face while you sing, and it’s very distracting.”

No hard feelings, apparently: Here she was to talk about the movie. “After they left, I could tell [Elvis] wanted to do it,” said Schilling. “But, as with so many of the things he wanted to do at that point in his life, he expected people would try to stop him.”

He was right. Some believe that Presley turned the role down because he didn’t want to play second fiddle to Streisand or because the subject matter hit a little too close to home. The real story: Presley’s longtime manager, Colonel Tom Parker, took over the negotiations and overplayed his hand. First, he reportedly asked Streisand and Peters for $1 million upfront, plus 50 percent of the profits.

But there was no way the film’s budget could cover two superstar salaries. (Instead, they offered points — a percentage of the movie’s profits — which was a better deal in the long run.) Parker also demanded star billing. (With Oscar-winner Streisand? Not likely.) Finally, he asked that all drug references be removed (impossible since drugs were one of the reasons for the character’s demise).

Presley didn’t care about any of that. He knew the role would give him a chance to show off his acting chops and help him find his way back into movies. But, as predicted, Parker would end up talking him out of doing the movie.

When A Star Is Born was released in November 1976, the critics weren’t kind, pointing out that it was impossible to buy Streisand (then 34) as an unknown ingénue hitching her wagon to a star.

Still, Streisand and co-star Kristofferson would win Golden Globes for Best Actress and Best Actor in a Musical or Comedy Motion Picture. The song Evergreen won an Academy Award for Best Song. What’s more, A Star Is Born would make an impressive $37 million at the box office.

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As the 1970s went on, Presley seemed resigned to following Colonel Parker’s uninspired lead, recording subpar material he wasn’t all that jazzed about.

How sad. Taking Streisand’s offer might have motivated and energized Presley, shaking him out of the stupor of his final years, and may even have given him a new lease on life. “This was not a man who waited for challenges,” said Schilling, “but a man who looked for them, even at this point in his career.”

Actually, Barbra Streisand and Elvis Presley would end up working together — in a sense — when Streisand released the 2014 album Partners, which included a posthumous duet with Presley.

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In an interview with Billboard to promote the album, Streisand talked about A Star Is Born and The King. “His career was slightly in decline, he was overweight, and I thought he was perfect to play that part,” she recalled. Leaving the rest of us with one of the great “What Ifs” in movie history.