The full-back sustained a shoulder injury whilst scoring a try in Wednesday's end-of-term defeat by the Barbarians at Murrayfield.
Glenn had been rated as a doubt for the opening encounter in Durban, in seven days' time. But by the time the squad flew into the city, the Scotland medics were much more upbeat.
Spokesman Graham Law said: "The doctors and physios are much happier with Glenn's condition. The injury seems to have settled down and at this stage there are no alarms about his prospects of playing next Saturday."