The Associated Press cites a law enforcement official with knowledge of the investigation into Jackson's death as saying Murray administered the Propofol, which authorities believe killed him.
Acording to TMZ, "Two days after Jackson's death, Dr. Murray told LAPD (Los Angeles Police Department) detectives he administered Propofol to the singer hours before he died ... this, according to multiple law enforcement sources.
"We're told Dr. Murray gave Jackson an IV drip of the powerful anesthesia. Police believe Dr. Murray simply wasn't paying attention when the singer's heart stopped beating.
"Authorities believe Dr. Murray may have actually fallen asleep during the time the drug was administered and may have awakened to find Jackson already dead from heart failure."
CBS News Correspondent Ben Tracy says it's not clear if Jackson ever woke up that next day after receiving the drug.
Jackson reportedly regularly received Propofol to go to sleep. He had a long history of prescription drug use and was under anesthesia for many medical procedures over the years.
Propofol is a powerful anesthetic that should only be used by specially trained medical professionals. Doses of it are said to have been found in Jackson's rented mansion.
The drug is used to sedate people in hospitals during surgery and should never be used outside of a hospital or a medical clinic, and if it was administered to Jackson in his home, the person administering it would have had to monitor the singer constantly while Jackson was on the drug.
Murray was with Jackson when he died June 25 and has been identified in court papers as the subject of a manslaughter investigation.
Murray's lawyer has said the doctor didn't prescribe or administer anything that should have killed Jackson.
But Murray has never denied giving the singer Propofol, Tracy reports.
Police recently shifted into a full-fledged criminal investigation, executing search warrants on Murray's clinic and storage unit and looking ahead to the kind of court case they could build against the physician, legal experts said Friday.
"This is no longer a cause of death investigation," said attorney Mark Geragos, who once represented Jackson. "This is about building a criminal case."
Jackson's prescription drug use so concerned his family, his brother Tito told Entertainment Tonight, he confronted him. "He said that he was fine. He was in good health. He was making a new record and looking forward to go back on the road and working," Tito told ET.
Tito added that he saw Michael three weeks before he died: "I wish I would have said 'Goodbye' in a different way," Tito said, "but I told him I loved him and he said, 'I love you more.' And those were the last words we had with each other."