Lythgoe told gossip website TMZ that he liked to see Sheen and funnyman Jerry Lewis on the panel next season.
Lythgoe may have been joking, but Sheen was taking it seriously. The actor told TMZ that he'd be on board if producers of his new FX series "Anger Management" sign off and "Idol" is willing to show him the money.
"If the numbers move the needle AND 'Idol' matches 20 percent of my weekly salary for Autism Speaks, JDRF, and the Boys and Girls Club … then the hell with it. As we say, pour the smoke."
"Idol" is reaching out to prospects in the event of a shakeup at the judges' table. Jennifer Lopez, Steven Tyler and Randy Jackson have not yet signed on for the 12th season. Nor has Lythgoe, for that matter.
In May, Lopez caused a stir when she told Ellen DeGeneres she might be leaving the show after a two-year run. "I don't know if I can go for a third year. I miss doing other things," she said.
Since then, Miley Cyrus, Nicki Minaj, Katy Perry and Black Eyed Peas members Fergie and will.i.am are reportedly being "considered" by "Idol" bosses, according to E! Online.
Former "American Idol" runner-up Adam Lambert has denied he's been in talks to serve as a judge, but admitted to The Hollywood Reporter that he'd "be more than flattered to have that conversation."