Dempsey has been stuck on the sidelines with a shoulder injury he picked up against South Africa in November but his imminent return is a boost for Glasgow and Scotland.
Dempsey trained for the whole of last week and Warriors defence coach Peter Murchie says he's on the verge of a return.
"He's had a good week training last week and he'll definitely be in contention (this weekend)," Murchie told Scotland Rugby News. "We just need to finalise the team over the next few days. He's been able to train every day last week and train well, so he definitely comes back into contention.
"Over the last few weeks, we've obviously built up pretty strong depth in the back row in terms of who's played with Jack Mann, Ally Miller and others so we've got good competition there. But Jack's definitely in the mix."
Adam Hastings is also making progress but it's unlikely he'll make Gregor Townsend's Scotland squad on Wednesday.
Asked about the stand-off's progress, Murchie said: "I don't know if he's ahead of schedule. He's training more. He's lifting weights, he's starting to run, but it'll be gradual. It'll have to go from skills for a few weeks into contact. So I'm not exactly sure on the timeframes.
"I don't think they've changed, to be honest, from where they were, but he's doing well. He's up and about, a lot less pain. He's able to do weights.
"He's able to get out there and run. I think he'll be able to join in a little bit of the skills this week. So that all shows it's going in the right direction, and they'll narrow the time frame when you see specialists, and they give you the OK to go and crack on with that contact.
"But at the moment, I don't think we're narrowing in on a specific week. He's going in the right direction."