Speaking on The Hollywood Reporter's 'Awards Chatter' podcast, he said: "I went in on a cattle call for 'Superman', and then it turned into a one-month audition experience where I was auditioning again and again and again.
"It looked like I was the director's choice for the role. I signed a three-picture deal at Warner Bros..
"This is a very early iteration of 'Superman' written by J.J. Abrams, called 'Superman: Flyby', I think is what it was called, and it never came to light."
Matt - who only came out publicly in 2012, a year after he got married - was then asked if his sexuality was a factor behind him not getting the job and he replied: "Yeah, that's my understanding. That was a time in the industry when something like that could still really be weaponised against you.
"How, and why, and who [outed me], I don't know, but yeah, that's my understanding."
In 2012, late author Jackie Collins claimed the 'White Collar' actor had been stopped from playing Superman because of his sexuality.
She told Gaydar Radio: "Matt Bomer, who is the most gorgeous looking guy and the star of White Collar, he had not come out of the closet, but people in the know knew he was gay.
"His audition tape went in and he called up the agent and somebody didn't like him and told [the producers] he was gay. They said, 'No, no, we can't cast you.' The reason he didn't get cast was because he was gay."
But insiders dismissed her claims and insisted Matt lost the part because of Brett's departure from the project.
A source told E! News at the time: "Matt was Brett's Superman. He would never have not cast Matt because he's gay. Brett knew Matt was gay. They're good friends.
"Matt not being Superman had nothing to do with his sexuality. It was because the director changed."
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Matt Bomer believes his sexuality cost him Superman role
The 46-year-old actor - who has three children with husband Simon Halls - was set to play Clark Kent and his alter ego on the big screen in the early 2000s and after a lengthy audition process, he was director Brett Ratner's choice for the role but he thinks his sexuality ultimately made the studio think twice about hiring him
