The 21-year-old failed to show up for the Garry Lynch Memorial friendly between Junior side Cambuslang Rangers and a Light Blues reserve team on August 11.
The no-show prompted an angry response from Rangers boss Ally McCoist.
He has told the player to keep his distance from the club's Murray Park training complex.
Cole has yet to make a competitive appearance this season and his last outing was in a friendly against Elgin City in July.
McCoist told the official Rangers website: "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."
Meanwhile, McCoist has revealed that Sam Kelly has made a positive start to his trial at Rangers.
The 19-year-old, a Republic of Ireland youth internationalist, has been released by Everton.
McCoist said: "He has come up and has looked great in training.
"He's very, very quick, he's comfortable on the ball and has a lovely left foot.
"He has fitted in with the lads well. We'll just monitor him and see how it goes."