The 18-year-old is still to make a start for Warriors but, with half a dozen appearances from the bench, and a striking cameo display in last weekend's win over Zebre, the time is coming.
"He's put his hat in the ring," said the Warriors assistant coach, Kenny Murray, in The Herald.
"The fact we signed him as a pro straight out of school shows how much we feel he is the real deal. There are not many players Glasgow or Edinburgh sign straight out of school."
With George Horne and Ali Price away with Scotland, the scrum-half berth is up for grabs. "Jamie's got an older adversary in Nick Frisby vying for that position but he'll be involved at some point," added Murray.
"There's a lot of competition, he's up against two international scrum halves. He has to oust them to get game time so that will be good for him.
"It will push his standards up. But's got a bit of everything. What I really like about him is that he's a very good tackler.
"George and Ali are good defenders and Jamie at such a young age is a good defender but he has that attacking ability. You think back to guys like Gary Armstrong who was an extra back row for Scotland.
"I reckon Jamie can have the same physicality in his game. The only thing he doesn't have is experience which is what he'll get going through these games.
"He's been patient. He knows there's a pecking order he has to push up but this is a window where young guys can get opportunities."
The Warriors lost out to the Dragons in the last meeting between the sides in an encounter which Murray described as one of the "worst performances of the year."
"Everybody has written us off, even (our chances of) getting in the play-offs," said Murray. "But people saying we are not going to get there is a good motivator for us.
"The last match against them (the Dragons) was just a poor performance all round.
"We couldn't keep hold of the ball, our decision making wasn't good enough and we didn't impose ourselves in attack or in defence.
"But we've got ourselves in a good position again and he boys are optimistic about the game."