Alcala was convicted last year of murdering four women and a 12-year-old girl in California in the 1970s.
He has also been charged with two murders in New York dating back to the 1970s.
However, Alcala claims he needs to remain imprisoned in California to work on his appeal - especially because he served as his own lawyer in the case.
It could be months before a judge issues a ruling.
After last year's conviction, authorities released more than 100 photos of young women and girls found in Alcala's storage locker, and prosecutors said authorities were looking into whether Alcala could be connected to cases in New York and other states.
The Associated Press contributed to this report.