“American Idol” producers are eager to hire Howard Stern to replace Simon Cowell as the show’s tough-talking judge, sources tell Page Six.

An insider said that producers of the hit Fox show say Stern, America’s highest-paid radio personality, is their top choice to take over from Cowell, who leaves at the end of this season. They approached the King of All Media after he repeatedly mentioned on-air that his exclusive Sirius XM Radio deal expires next January and he was open to other offers. Cowell was paid $50 million a year.

A source connected to “Idol” said, “It’s one of the few shows that could compete with Stern’s $100 million-a-year Sirius contract, and ‘Idol’ bosses think he’d be even nastier than Simon.

“They know he would be great TV and would clash with the other judges such as Ellen DeGeneres and the contestants. ‘Idol’ will do what it takes to sign him.”

But a second source told us Stern hasn’t made the “Idol” talks easy, and has been giving out mixed messages about his intentions.

“Despite what he’s been saying on-air, Howard isn’t ready to leave radio and would like to stay on at Sirius,” the source said. “We believe this is a ploy to make Sirius pay up and keep him on his huge contract. But if Sirius can’t pay him the money he wants, he may negotiate to film ‘Idol’ on the side.”

Stern is also believed to be reluctant to commit to a show that would require him to tour the US as a judge and spend much of the year in Los Angeles.

He recently said, somewhat cryptically, “I was approached by a major TV network to take over a TV show and leave here and do that next year — and I did turn it down . . . I’m not even sure if I want to be working. I’m waiting to see what happens.”

Calls to Stern’s agent and producer were not returned. A rep for FOX declined to comment.