CBM says

This was a pretty wild rumor that I'm surprised is still making the rounds but it appears that it's simply not true, Cooper will not be Lex Luthor.

And there you have it. I'm definitely inclined to believe the words of an industry veteran like Kurt Orzeck over the site where this rumor originated. While Cooper definitely has his fans out there, I personally think he isn't right for the role. Who would you guys like to see portray Lex Luthor on the big screen? If Luthor does not cameo in the first Superman reboot and the film is a success, it's a strong likelihood that Luthor will show up in a sequel. Hopefully we get the manipulative, evil mastermind from the comics and not the camp, real estate tycoon we've previously seen in prior Superman films. (Bradley Cooper, Cinema, Man of Steel)