Speaking in a live news conference today, an officer confirmed a knife was found on the estate in the late 1990s by a former LAPD officer - who was either retired at the time, or is believed to have retired shortly after.
They told reporters: "Within the last month, the LAPD became aware of an item that was allegedly recovered by a citizen at the Rockingham Estate property, possibly during the demolition of the site."
However, when asked if double jeopardy would be in place - meaning Simpson could not be charged again in the murder case - the officer admitted he believed that the former star "could not be charged again".
He said: "I'm not an attorney, but being a police officer for 30 years it's my understanding that double jeopardy would be in place here so we could not charge Mr Simpson with the homicide as he's already been charged and acquited."
Speaking about the item found, police confirmed it was a "knife", but could not describe it any further.
They added: "My understanding is that it's a knife, not a machete."
They went on: "The investigators have asked that we don't be very descriptive about the knife. They haven't actually told me so I don't accidentally tell you. We need to determine if this is evidence."
And they confirmed it was handed to the former LAPD officer, believed to have been retired or close to retirement at the time, in the late 90s, when they were working as a motor officer.
The officer is believed to have been off duty at the time, and they added: "I do not know if he was retired when he received this item, or if he was still an LAPD officer and retired after - we are looking into that."
The case has remained open over the last decade, as the LAPD said in the conference: "Unless there's an arrest or conviction to prove we have closed the case, the cases remain open, thats where we are with this case."
The investigation will continue, with forensic tests underway on the knife.
They said: "The investigators will continue to look at this. It is being treated as we would all evidence and has been submitted to our lab. They are going to study it and examine it for all forensics, including DNA and hair samples and that is ongoing as we speak."
Asked his own response to the news, the officer admitted: "I was really surprised. I would think that an LAPD officer, if it's as accurate as we are being told, would know that any time you come into contact with evidence that you should and you shall submit that to investigators. So I don't know what the circumstances are why that didn't happen, or if this whole story is bogus from the get go, involving a whole variety of people.
"We are looking into that, but I was quite shocked.