Nicki Minaj’s “American Idol” contract is almost signed, but her deal with Pepsi is holding it up. Pepsi sponsors her tour, but “Idol” is sponsored by Coca–Cola, so they’re hashing out how to get around the sticky cola issue. We’re told “Idol” execs want to announce Minaj as a judge as soon as possible, before the auditions start filming in the next week or two. Sources say producers “want to see that drama between Nicki and Mariah Carey. It’ll make for good TV.” It seems there will now be four judges — country singer Randy Travis was in consideration until he had his “epic booze-fueled meltdown.” Now Keith Urban and Brad Paisley are in talks. “Idol” producers had hoped to get Enrique Iglesias, but, “He’s a private guy and doesn’t want to expose his life to the show,” our source said.