Jim McCafferty, 71, who was involved in football in Scotland and Ireland from the 1980s, was arrested in Belfast by the Police Service of Northern Ireland (PSNI) after walking into a police station.
It follows an interview that McCafferty, originally from Wishaw, North Lanarkshire, gave to the Irish Mirror newspaper.
McCafferty, who now lives in Belfast, was formerly a kit man at Celtic, Hibernian and Falkirk.
Detective Superintendent Deirdre Bones, from the PSNI’s public protection branch, said: “A 71-year-old male has been arrested by detectives after presenting himself at a station in Belfast.
“He was arrested on suspicion of sexual offences against children in Northern Ireland. He is currently helping police with their inquiries.”
In Scotland, police say they have received information about alleged historic offences and will investigate.
A police spokesman said: “Police Scotland has received a report of non-recent sexual abuse and will commence inquiries to establish the full circumstances surrounding this matter.”