Jennifer Lopez and ‘American Idol’ producers played a cat-and- mouse game over the singer’s future on the TV talent show that revived her career and sent her to the top of a global celebrity power list. ‘American Idol’ producer Nigel Lythgoe said Lopez must decide whether to sign up as a judge for a third year or go off in a new direction. In what some industry watchers saw as a negotiating ploy, Lopez sparked a media frenzy this week when she said she wasn’t sure about renewing her contract, and sources close to her said she was “just too busy” to commit to the show. She made similar comments a year ago before signing a new one-year deal. Lythgoe told reporters on a conference call that all three ‘Idol’ judges – Lopez, Steven Tyler and Randy Jackson – had busy careers outside the talent show, but he would be happy to have them all back. He said ‘Idol’s’ long schedule of nationwide auditions, plus four months of live shows, was tough for everyone to juggle. Tyler’s band Aerosmith has a new album coming out and a summer tour. “It’s got to fit everybody, and it’s difficult. You have got to start making decisions. Do I want to carry on doing this? Do I want to go off and make movies? For her part, Lopez denied media reports that she had already decided to quit the show after the current season ends. “There is no truth to reports that say I am definitely leaving ‘Idol’,” the pop singer Tweeted. “All I said was I haven’t decided what I am doing next year.” Lopez was named the most powerful celebrity in the world by Forbes this week, citing record sales, multiple product endorsements and social media buzz.