While his chances of featuring for Scotland against Ireland in the final round of the Six Nations Championship remain slim, the decision not to go under the knife is a boost for Glasgow Warriors.
Assistant coach Scott Forrest told Scotland Rugby News: "Jack's going down the non-surgical route. So, that's probably a more conservative approach just in terms of the nature of an injury he had and there was a decision to be made there.
"So, best case scenario, he could be back in a matter of weeks for us, which obviously, that would be huge. But, same with any injury, there are no guarantees he's going to go down that route just now. And then obviously, it just depends on how he responds with his rehab."
Forrest admits a rapid return in time for Dublin would be exceptional but hasn't ruled it out.
"That's not really one I'm in a position to answer. I think with the nature of the tendon injury on his bicep, people react in different ways.
Obviously, the fact that he doesn't need to get surgery on this, because it's at the top of the bicep, not the bottom, then that's a positive. But ultimately, it really just depends how he reacts over the next week to 10 days to determine how quickly he'll be back.
"If he's back for Ireland, that would be probably one of the quickest recoveries, but like I say, everyone responds in different ways. I'm not going to stand here and be able to say a 'yes'or a 'no' but you can't rule him out altogether.
"I think any sort of chance is probably enough of a chance for Jack just to push on and focus on that."
Elsewhere, Glasgow will be boosted for Saturday's URC trip to Connacht, with Kyle Rowe, Stafford McDowall, Ollie Smith, Gregor Hiddleston and Alex Craig all returning from Scotland duty, although Adam Hastings has not been released.