The governor said he would meet Dec. 8 in a private hearing with Williams' lawyers, Los Angeles County prosecutors and others involved.
Schwarzenegger has the authority to commute a death sentence to life without parole, but he is not obligated to hold a hearing. In Schwarzenegger's case, he decides clemency requests on a "case-by-case basis," spokeswoman Margita Thompson said.
Two other clemency petitions have come before Schwarzenegger. Neither was granted.
Williams, 51, faces a lethal injection on Dec. 13 for the 1979 slayings of a Whittier convenience store clerk and three people at a Pico Rivera motel. He has maintained his innocence and has asked the California Supreme Court to reopen his case, alleging shoddy forensics wrongly connected him to three of the murders. The Supreme Court hasn't ruled on the petition.
Los Angeles County prosecutors and victims' relatives have demanded his execution.
Along with asking Schwarzenegger to commute Williams' death sentence, his lawyers submitted what they said were signatures of 32,000 people supporting his petition for clemency.
Supporters, including rapper Snoop Dogg and Ras Baraka, the deputy mayor of Newark, N.J., have urged Schwarzenegger to spare Williams' life so he can continue his work with young people as an anti-gang activist.
At alast week, CBS News correspondent John Blackstone reported that the inmate's supporters promised growing demonstrations over the next three weeks, but there are those who remain unconvinced Williams has changed.
"He has multiple incidents where he has been involved in violent acts while here on death row at San Quentin – batteries, assault on staff," said Lt. Vernell Crittendon, a San Quentin Prison spokesman.
Williams founded the Crips with a childhood friend in 1971 in Los Angeles, where the gang battled rivals for territory and control of the drug trade.
In prison, however, Williams gained international acclaim for co-writing children's books about the dangers of gang life. An award-winning television movie starring Jamie Foxx, "Redemption," was based on his life.
Schwarzenegger, in dealing with the two previous clemency requests, denied a hearing last year for Kevin Cooper, whose execution was later stayed by a federal appeals court, and held a public hearing this year for Donald Beardslee but declined to spare him.