The Los Angeles district attorney's office said Monday it would not file charges against Shaw, who was the subject of a domestic violence investigation stemming from an August incident at his apartment.
Shaw has been suspended from team activities since August, when he told USC officials a fabricated story about how he suffered ankle injuries.
USC has said it would conduct its own investigation regarding Shaw before determining if he would be allowed to return to the team. Officials gave no timetable for when it would be completed.
"It's in the university's hands," Sarkisian said, "and it hasn't really gotten to me yet."
USC plays UCLA on Saturday and concludes the regular season Nov. 29 against Notre Dame.
Shaw is a senior and team captain.
"It would be great for Josh," Sarkisian said when asked how much he would like to have Shaw back. "It's your senior year, you want to play, especially against your two rivals.
"We've played 10 games without him so we have a pretty good understanding of who we are. It would be nice for Josh. It would be nice to have him, but again we've played 10 games without him."