Press reports claim the former midfielder, a team-mate of McCoist's, has been told to stay away while an investigation is carried out into last summer's transfer dealings.
However, speaking at his pre-match press conference ahead of Saturday's trip to Montrose, McCoist refused to go into more detail.
"Neil has been suspended by the club pending an investigation," he said. "It's a really sensitive matter and that's all I can say on it."
Murray's suspension follows the recent departures from the third division club of youth team coach Tommy Wilson and long-time physiotherapist Pip Yeates.
Asked if he was concerned over the staff changes, McCoist said: "My concern is that we have to be in position ready to go for the start of next season.
"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. We have to be ready for that... and we will."