Sky Sports states The man, understood to be former Celtic Boys Club official Frank Cairney, is expected to appear in court on Wednesday.
A spokeswoman for Police Scotland said: “An 81-year-old man has been detained and charged in connection with non-recent sexual offences.”
The sport has been hit by claims from former players across the UK that they were abused by people in positions of authority.
Police Scotland launched a major inquiry into non-recent child abuse in youth football at the end of last year.
A number of professional clubs have started internal investigations, while the SFA has set up an independent review into allegations across the game in Scotland.
