McCafferty, 71, also worked at Celtic and Falkirk.
A Police Scotland spokesman said: “Police in West Lothian have received a report of non-recent sexual abuse and will commence inquiries to establish the full circumstances surrounding this matter.”
A spokesman for Hibernian said: “Everyone at the Club was shocked to read this man’s comments about his time in football. Hibernian will assist the police with their inquiries in every way that we can, and we would urge anyone who may have any information which can assist with inquiries to contact Police Scotland on 101. We would also remind anyone who may have been a victim of abuse that a helpline has been set up, 0800 023 2642 or via email at [email protected] “