The 26-year-old ruptured his anterior cruciate ligament in April last year and has been recovering ever since.
Hamill was reportedly set to resume training this month but McGlynn says his progress has been hindered by pain in his knee.
He told the Daily Record: "Jamie was backed off a wee bit because his knee was giving him a bit of pain.
"He is now back working in the rehabilitation room with the physio Rob Marshall and we'll just have to wait and see how he gets along.
"If he can progress then he will get back into running and eventually get back training with the first team."