The physician was handed a four-year prison sentence last year, after being found guilty of the involuntary manslaughter of Michael Jackson.
TMZ reports that Murray has asked a judge to send him to a state prison, because his stay at the LA County Jail is taking a toll on his health.
He allegedly told his lawyer Valerie Wass: "I may not make it out of here alive. This is a very dangerous place. I'm in here dying. The system is intent on killing me."
According to his lawyers, Murray is allowed to leave his cell once a month and receives fresh underwear once a week, circumstances that the doctor believes have led to constant headaches.
Murray has apparently claimed he has never received headaches before, and fears he may have a brain tumour.
This is not the first time the ex-physician has asked to be released or transferred from jail.
Murray filed paperwork for release in January, citing "improper exclusion of defence evidence and witnesses" during the court proceedings. He was later denied.