Gordon Neely, who was also a youth coach Hibs in the 1980s, was said to have been dismissed after a meeting with the then Rangers manager, Graeme Souness.
Neely, who died two years ago, was alleged to have spoken inappropriately to a teenager. The boy then told his father who contacted the club.
There is no suggestion of physical contact.
A statement from Rangers said: “Rangers is now aware of an alleged incident involving an individual who worked very briefly for the club more than 25 years ago. It’s understood the individual was dismissed immediately and that the police were informed.
“Rangers wishes to stress that all employees adhere to the strictest codes of conducts, especially when dealing with children and young people.”
The incident was said to have been reported to police at the time, however Police Scotland has not approached the club.
Reports at the weekend said that Neely was one of the game’s most sought-after youth coaches when he left Hibs in 1986 to join Rangers.
A Hibs spokesman said: “We are not aware of any complaints being made at the time but that does not mean we should be complacent.”
The club was unable to comment as to whether it would be looking into the matter further.
Neely began his coaching career with Edina Hibs, now known as Portobello Community Football Academy, and Hutchison Vale boys’ clubs in Edinburgh.
Hutchinson Vale club leader Tam Smith said he had not heard of any allegations of misconduct against Neely.
He said: “I’ve heard of him and I know he was well known at the club before my time.
“But I’m not aware of any allegations being made about his conduct while he was here.
“I am aware things have been tightened up very much for the better. In those days, anyone could start a football team and no-one checked their background.
“We can never be complacent but in common with 90 per cent of clubs, we now have a child protection officer and I think we take better care now than in the past.”
Mr Smith, who joined the club in 1989, added: “We have to make sure we keep giving kids opportunities – and that we always put their interests and safety first.”
The Scottish FA said it was working with the police to “ensure a co-ordinated response” to the wider investigation. A Police Scotland spokesman commented: “We have received reports in connection with non-recent child abuse within football.”
The incident has emerged as police across the country continue to probe allegations of historical sex abuse in football.
Last month former Crewe Alexandra youth coach Barry Bennell was charged with eight sex offences against a boy aged under 14.
The offences are alleged to have been committed between 1981 and 1985.