The document indicated the conversation allegedly was between two people with Hernandez when he picked up Lloyd from his Boston apartment June 17, just hours before a jogger found Lloyd's body in a North Attleborough, Mass., industrial park not far from Hernandez's home, CNN reported.
Hernandez and the two other men are in custody.
Prosecutors have accused Hernandez, a tight end with the New England Patriots until they released him soon after his June 26 arrest, of orchestrating Lloyd's death.
Hernandez, 23, remains in a Massachusetts jail. He pleaded not guilty to murder charges.
The information in a document filed in Florida could help Massachusetts authorities as they build their case against Hernandez, CNN said.
In Miramar, Fla., Ernest Wallace turned himself into police June 28 after seeing news reports that an arrest warrant had been issued for him in the killing. He was charged with being an accessory after the fact to murder.
The other man arrested in the case, Carlos Ortiz -- who is from Hernandez's hometown of Bristol, Conn., -- told authorities Wallace told him Hernandez fired the shots that killed Lloyd, a document cited by Miramar Police spokeswoman Tania Rues said.
CNN said it didn't see the court document filed in Florida.
The information from Florida was revealed on the same day a number of documents pertaining to Lloyd's death were released in Massachusetts.
Among the documents released on a judge's order was a recounting of a conversation between police and Hernandez at the football player's home after Lloyd's death but before Hernandez was arrested.
The documents indicated Hernandez "became argumentative" when talking to officers.
"Mr. Hernandez did not ask the officers whose death was being investigated. Mr. Hernandez's demeanor did not indicate any concern for the death of any person."
In contrast, when police told Hernandez's fiancee about the death of Lloyd, who was dating her sister, "she immediately began to cry," the documents indicated.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys