According to kicker, the 18-year-old is expected to rejoin full team training this week and could feature for a handful of minutes when Bayern Munich host VfB Stuttgart on Friday evening.
Karl tore a muscle fibre in his left thigh during World Cup training camp preparations in June and has been sidelined ever since.
Gnabry, 31, will have to wait a little longer. The forward suffered a torn adductor in April and, according to the same publication, is unlikely to be fully reintegrated into full team training until at least the end of this week — a timeline that comes too soon for the Stuttgart-born forward to feature in Bayern's season opener.
He has been working through his rehabilitation programme alongside fellow absentees Jamal Musiala and Alphonso Davies at Bayern's Säbener Straße training base while much of the squad completed the Audi Summer Tour in Asia.
Karl's return would be a significant boost for the Bundesliga champions after a breakout campaign in which he emerged as one of Germany's brightest young attacking talents, combining with Gnabry for a combined 25 goal contributions last season.
Both missed this summer's World Cup in North America as a direct result of their respective injuries, with Karl forced to withdraw from the Germany squad after picking up his injury in camp and Gnabry ruled out having been sidelined since the spring.
Bayern have already negotiated the opening weeks of the new campaign without their full squad, having beaten Borussia Dortmund away in the Franz Beckenbauer Supercup without either player available.
Jamal Musiala, who also missed that fixture, is expected to return to full training in the coming days and could likewise be in contention for a recall against Stuttgart, giving Vincent Kompany's side a welcome boost in attacking options as the Bundesliga champions begin the defence of their title.