DeWine said coaches are among officials required by state law to report suspected child abuse. Saccoccia has not commented.
Steubenville city manager Cathy Davison said residents want to see justice done, and the city will be better off going forward because of the wider investigation.
"Football is important in Steubenville, but I think overall if you looked at the community in and of itself, it's the education process, the moral fiber of our community, and the heritage of our community, that is even more important," Davison told The Associated Press.
Steubenville schools Superintendent Mike McVey released a statement Monday reiterating his position that the district was waiting until the trial ended to take action. He declined to address the grand jury investigation.
"What we've heard so far is deeply disturbing," McVey's statement said. "At this time, we believe it is important to allow the legal process to play out in court before we as a school district make any decisions or take action against any of the individuals involved with this case."
It's unclear what could happen to the school's sports programs if coaches were charged. Sanctions against teams or programs typically involve violations of rules related to playing, such as improper recruiting of student-athletes or playing ineligible athletes, said Tim Stried, spokesman for the Ohio High School Athletic Association.
"The incident that happened was not during a contest, was not even at school. No playing rules were violated, and it didn't have anything to do with eligibility or recruiting," Stried said.
Mays and Ma'Lik Richmond were charged with penetrating the West Virginia girl with their fingers, first in the back seat of a moving car after a mostly underage drinking party on Aug. 11, and then in the basement of a house.
Mays, 17, and Richmond, 16, were sentenced to at least a year in juvenile prison for the rapes. Mays was ordered to serve an additional year for photographing the underage girl naked.
They can be held until they turn 21.
Special Judge Thomas Lipps recommended the boys be assigned to Lighthouse Youth Center-Paint Creek in Chillicothe. The Ohio Department of Youth Services contracts with the secure, residential center. Lipps said it had a strong program for treating juvenile sex offenders.
Associated Press writer Kantele Franko contributed to this report.
Andrew Welsh-Huggins can be reached on Twitter at https://twitter.com/awhcolumbus