The 21-year-old was due to be part of the squad for the Garry Lynch Memorial friendly between junior side Cambuslang Rangers and a Light Blues reserve team on August 11.
But Cole failed to report for the game and following a discussion with manager Ally McCoist, he is not currently training at Murray Park.
The defender has found himself fall out of favour in recent weeks after being included in the squad for the Northern Tour matches at Brora and Elgin City last month.
He hasn’t featured for the first team since that second fixture at Borough Briggs on July 10 and isn’t being considered for selection at present by McCoist.
The Gers boss said: “Darren failed to report for the game against Cambuslang but he’s not following a fixed suspension.
“He didn’t attempt to contact anybody at all to let them know he wouldn’t be coming to the game and it goes without saying we thought his conduct was totally unacceptable.
“I’ve asked Darren to stay away from the club until further notice and until we discuss what our next course of action will be.
“I’ve already had a chat with the player to register my disappointment with him and to ask him for an explanation.
“What was said there will remain between him and I but I’ll also need to have a talk with my staff to decide what we will do now.”
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