However, the pre-season games will come too soon for Zander Fagerson.
Dempsey hasn't played since Scotland's Six Nations win over Wales at Murrayfield in March.
A hamstring injury wasn't thought to be too serious at the time but Dempsey ended up missing the rest of the season including Scotland's summer tour to give him as much time as possible to recover.
Dempsey has been fully involved in training with Glasgow and is expected to feature in the coming weeks. Glasgow take on English champions Bath at The Rec on Saturday before hosting Northampton Saints at Scotstoun the following Friday.
"Jack's been fully involved in rugby and is looking really sharp," Glasgow's new assistant coach, Scott Forrest said in The Scotsman. "He's been fully involved through pre-season, and is probably someone that will be involved at some point in one of these pre-season games. He's trained really well and players of that calibre are the guys that we want to get back onto the pitch."
Forrest believes it was the correct decision to give Dempsey an extended break.
"I'm not a medic but I do know that it was probably the best thing for him as an individual just to get that extra time, and I suppose all I'm seeing now is what he's like on the pitch, and he's training fully now," said Forrest.
"Could he have gone for Scotland? I don't know, around the medical decisions there, but I know the best thing for him was just that he was given that extra time, and I think hopefully we're going to see the benefit of it come the start of the season."
Forrest provided an update on Fagerson who suffered a calf injury in training in April. The prop ended up having to withdraw from the British and Irish Lions tour of Australia.
"Zander's not fully back into rugby," said Forrest. "He's very much on track in terms of his return but he's not fully back in."
Duncan Weir is also close to a return after undergoing surgery on a shoulder at the end of March. "He's probably got another week or two around all the return to play and contact protocols that he still needs to get through .So, he's still got a couple of boxes to tick, but again, he's on track," added the coach.
Warriors are planning to send a relatively inexperienced squad to play Bath at The Rec.
"This weekend for Bath will be mainly the academy, the non-international boys, the guys that have been in since the start of pre-season," said Forrest.