Producers of American Idol are not about to take shock jock Howard Stern up on his offer to leave radio behind and instead replace Simon Cowell on American Idol , Cowell himself indicated Thursday. Speaking to reporters during a conference call, Cowell maintained, "I am fairly certain there hasn't been an approach at any time for Howard to do the show." On his Sirius radio show, Stern has been riding a wave of rumors that he is being considered for the lead judge's chair when Cowell leaves the show at the end of this season. "Name a person who could bring more excitement to [American Idol] than me," he said last week. But Cowell listed the criteria the producers of the show have in mind in their search for a replacement. "You've just got to find someone who can actually make a difference to the contestants, who is not afraid to speak their minds, who is prepared to be honest and occasionally blunt, but not to be gratuitously rude." Stern, he said, doesn't fit those criteria, "but he obviously wants the job! Good luck to him."