Murray, 60, gave Jackson a lethal dose of anesthetic while he was treating him, leading to Jackson's death at age 50 in 2009.
Murray was convicted of involuntary manslaughter and sentenced to four years in prison, but is scheduled to be released Oct. 28, after serving less than half the sentence.
"Murray is the killer of Michael in their eyes," a family source told the Mirror. "He cost them their son and father. For him to get out in two years is an insult. They still feel he should have been tried for murder."
Murray has been in solitary confinement since he was jailed in 2011.
A source the Mirror described as close to Murray said he "has been a model inmate and the authorities have granted him an early release due to that good behavior and the overcrowded California jail system."
Michael Jackson's mother, Katherine Jackson, is suing concert promoter AEG for wrongful death, claiming the firm did not properly investigate Murray before employing him. AEG argues Michael Jackson hired Murray.
Murray is appealing his conviction.