It has been alleged Michael was administered the sedative by Murray some time after midnight on June 25, the day the ‘King of Pop’ died of a suspected cardiac arrest.
Police are still waiting for the results of toxicology tests carried out as part of the autopsy, but are reportedly already working on the assumption that Propofol, also known as Diprivan, caused the pop superstar’s heart to stop.
Last week, it was revealed Murray was being investigated for manslaughter in relation to Michael’s death.
His office in Houston, Texas, and a storage unit were raided, with police removing items including a computer hard drive and drugs including a muscle relaxant and appetite suppressant.
Murray’s lawyer Ed Chernoff has insisted his client did not give the ‘Thriller’ singer anything which could have caused his death.
However, it has also been claimed Murray has admitted to police he gave Michael Propofol.
Gossip website TMZ reports: “Two days after Jackson's death, Dr. Murray told Los Angeles Police Department (LAPD) detectives he administered Propofol to the singer hours before he died... according to multiple law enforcement sources.”
It has been suggested Murray may have fallen asleep while the singer was receiving the drug.
Meanwhile, Michael’s brother Tito has confirmed the singer’s body is being held at Forest Lawn Memorial-Parks and Mortuaries, where the family held a private memorial service for him.
It has also been claimed a custody agreement for Michael’s three children – Prince Michael I, 12, Paris, 11, and seven-year-old Prince Michael II – is close to being finalised.
Michael’s mother Katherine Jackson currently has temporary custody of the kids, and is understood to be in the process of arranging for Prince Michael I and Paris to meet their biological mother Debbie Rowe.
Michael’s lawyer L. Londell McMillan said on US TV show ‘Today’: “We'll be making an announcement very soon. I want to say the parties have been very responsible. Debbie Rowe, her lawyers, Mrs. Jackson have been very thoughtful, very caring, very prudent, and we do believe we're very close to reaching an agreement, and this swirling speculation is just swirling speculation.
“We've kind of gotten together, and we've been thoughtful and prudent and we're working on an agreement that's going to be not just what's best for Debbie Rowe or Mrs. Jackson, but what's best for the two children that Debbie Rowe had.
“What's best for the children is what Michael wanted and what has been happening: Mrs. Jackson to have custody of these children.”
