The response is being co-ordinated at a UK level because many incidents involve more than one police force area, Mr Gormley told a Scottish Police Authority meeting.
He described the situation as “fast-moving and fluid which requires both sensitive policing and strong partnership work”.
Mr Gormley said: “At the point this information was pulled together for me this morning, we’ve received 109 referrals which relate to child sexual abuse within football.
“Specialist officers from the national child abuse investigation unit are assessing the information coming into us and determining the most appropriate response.”
He added: “While capacity may be tested over the coming weeks and months, I’m genuinely confident that the strong partnerships built up over many years will ensure that we continue to provide a complete and holistic service that meets the needs of children and adults who have been abused during their childhood.”