Van der Sloot, 22, is being held in Peru in the death of 21-year-old business student Stephany Flores.
He's also the chief suspect in the disappearance in Aruba five years ago of Alabama teen Natalee Holloway. Van der Sloot was taken into custody and questioned twice in that case, but has never been charged.
Peruvian police say van der Sloot confessed to killing Flores, telling them, reports CBS News Correspondent Elaine Quijano, he did it because she saw information about Holloway on his laptop.
Days before leaving for Peru last month, van der Sloot was targeted by the FBI in the Holloway case.
In April, he allegedly offered a deal to Holloway's mother: He'd disclose the location of her daughter's body in exchange for $250,000.
Private investigator Beau Dietl was brought in by the Holloway family.
He told CBS News van der Sloot "admits to pushing Natalee down, where he hits her head and she dies. That's what he states."
The FBI then launched the sting, Quijano says.
On May 10, van der Sloot was given $25,000, but federal officials say he provided false information about the location of Holloway's body.
The FBI says it didn't move in because its case "wasn't sufficiently developed."
Van der Sloot left Aruba and wound up in Peru, where he's accused of taking Flores' life.
On "The Early Show" Thursday, Dietl took viewers inside the FBI sting.
As he tells it, van der Sloot contacted the Holloways, saying "his father had just died in January and he wants to come clean and he wants to tell everybody where he buried Natalee Holloway" - if they give him $250,000.
Dietl says his firm arranged to meet van der Sloot in Aruba, then let the FBI know what was going on.
It was at that point, says Dietl, that the sting was put together.
And, he asserts, Aruban officials dropped the ball by not arresting van der Sloot - again, before he was off to Peru.
And, Dietl observed, "This guy's been all over the world in the last five years. Thailand, everywhere. This is a homicidal maniac. I've met him. I looked in his eyes. This guy we should be checking Interpol and the FBI should be checking where he's gone all over this world. You've got a serial killer here. I think."
To see the entire Dietl interview, click on the video below: