The back-row has been sidelined with a shoulder injury sustained in Scotland's Autumn Nations Series defeat to South Africa but he's nearing a timely return to fitness.
He's unlikely to feature against Racing 92 at Scotstoun in the European Champions Cup on Friday - although it's yet to be ruled out - so Glasgow's trip to Harlequins in a two weeks is more realistic.
"Jack is a hell of a lot closer than he was before Christmas," assistant coach Nigel Carolan confirmed on Scotland Rugby News.
"Every week he's getting a bit closer. So we hope that he's training fully this week. It could be a week too early for him, but we'll know as he's joining training collectively. It's good to have him back."
Long-term absentees Sione Valianu and JP du Preez are close to making their returns, while Adam Hastings is making progress.
"Sione and JP du Preez are maybe a couple of weeks away as opposed to days away," Carolan added. "Again it's good to have them back with their dates getting closer. They're valuable assets to the club and they'll be a welcome return when they do make it back.
"Adam is fit and back training, but it's just more precautionary. He was wired up in the jaw until a couple of weeks ago. Again it's a bit of management and building back up his confidence around contact. It was a horrendous injury and it's certainly one that we're not going to rush back."