A judge sentenced Davis, now 70, to life in prison in 1972 for his role in the murders of two men. He was not involved in the infamous Sharon Tate murders.
After serving more than 40 years in prison, the parole board is recommending that Brown approve Davis' parole. The governor has 30 days to make a decision. His options are to affirm, decline, modify or decline to review, which would allow the parole to take effect, an official said.
If he is freed, Davis will go to transitional housing associated with religious groups in Los Angeles County.
Former Gov. Arnold Schwarzenegger rejected a previous parole recommendation for Davis. Los Angeles District Attorney Jackie Lacey sent a letter to the board last week opposing Davis' release.
Davis became a born-again Christian in prison and ministered to other inmates, married a woman he met through the prison ministry, and has a grown daughter. The couple recently divorced. He also earned a master's degree and a doctorate in philosophy of religion.
The Associated Press contributed to this report.