Rangers chief scout Neil Murray has been suspended pending a club investigation.
After confirming the 40-year-old former Ibrox midfielder's suspension, Rangers manager Ally McCoist said: "It's a really sensitive matter and that's all I can say on it."
Two other members of Rangers' backroom staff have departed in recent weeks.
Reserve coach Tommy Wilson joined MLS side Philadelphia Union and physio Pip Yeates left after five years at Ibrox.
Murray was part of the Rangers' nine-in-a-row squad and left to join Sion in 1996 before spells in France and Germany and a return to Scotland.
Asked about concerns over changes to his backroom staff, McCoist said: "We have to be in position ready to go for the start of next season, that's my concern.
"Staff at football clubs, and in any work force, come and go. I fully appreciate that.
"That said, in terms of the recruitment of our players, the next two or three years will be the most important time in the club's history.
"So we have to be ready for that and we will be."