Chicago- Jack Palladino — a private investigator once hired by Bill Clinton to track down women he’d been linked with — testified Thursday that a star witness in the R. Kelly case wanted a $300,000 bribe to keep quiet.

Kelly hired Palladino in 2002 to help in his defense after he was charged with child pornography. The R&B star has pleaded not guilty.

Palladino, of San Francisco, took the stand to discredit Lisa Van Allen, who testified Monday she had threesomes with Kelly and the underage girl who allegedly appears in a sex videotape with the singer. Palladino traveled to Atlanta in March to interview Van Allen, he said.

In a meeting at the Four Seasons Hotel, Van Allen’s fiance Yul Brown told the P.I. that Van Allen had a $300,000 book deal to tell her story, according to Palladino.

“I didn’t believe there was a book deal. The $300,000 was a coded way to get money from my client,” Palladino testified.

Palladino said he told Brown that Kelly would not pay them. He denied threatening the couple — disputing Van Allen’s testimony. But he said he recorded the conversation.

“I had a very good idea they would try to extort money,” Palladino said.

On cross-examination, prosecutor Robert Heilingoetter noted neither Brown or Van Allen ever asked for money.

“I’m trying to figure out where this extortion is, except somewhere between your ears,” Heilingoetter said.

But Palladino testified the two repeatedly said they wanted to do what was best for their family — and urged the investigator to talk to Kelly.

“There’s little doubt about what that meant,” Palladino said.

Heilingoetter noted Palladino was paid $15,000 for the Atlanta trip. “So for $15,000, you found out that Yul Brown wanted to do what’s best for his family. Nice work, detective,” Heilingoetter said.

Also Thursday, jurors were shown footage from the video in which two headless bodies are having sex — an image meant to bolster the defense’s claim that the tape could have been faked.

Defense expert Charles Palm said it had taken him “a couple of spare hours” to do the work digitally. He later said it would take “a couple of months” to fake the entire 27-minute sex tape. A prosecution expert said it would take 44 years.

But, Palm said, “even the untrained eye” would be able to spot the tricks he performed. When prosecutors played him several sequences from the sex tape, Palm said, “I don’t see anything that would indicate fakery.”