The 42-year-old 'Dallas Buyers Club' star was tipped earlier in November to be a leading candidate for director David Ayer's film, reported MTV online.
'Suicide Squad' centres on super villains being thrown together by the US government as a black ops team to work off their prison sentences.
Will Smith, Ryan Gosling, Tom Hardy and Margot Robbie have been rumoured to be in talks for the film, while Cara Delevingne has been linked to the role of the Joker's sidekick Harley Quinn.
"You know there's a film called 'Fight Club'. You know what the first rule is, don't you? Enough said," Leto said.
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Leto was referencing Brad Pitt's iconic 'Fight Club' dialogue: "The first rule of Fight Club is: You do not talk about Fight Club."
"I've been reading scripts. It was a pretty incredible last year. There was this cool event called the Oscars. That basically changed my life and for a wonderful film that I was proud to be a part of - 'Dallas Buyers Club'. I'm not really in a hurry to jump into another film, unless it's something that I absolutely can't say no to.