The 40-year-old required emergency medical assistance after collapsing at the club's training complex in October. He was subsequently taken to hospital, where the cause of the incident was identified as a meningeal irritation.
Kompany has since been discharged and is recovering at home. His condition has improved in recent days, but Bayern are determined not to rush his return, with his health remaining the priority.
According to the Abendzeitung, club officials are considering whether the Belgian could resume work at the training ground after the international break, potentially in the days leading up to Bayern Munich's Bundesliga meeting with 1. FC Köln on November 20.
Any return will depend on approval from the medical department. The club will follow the advice of the doctors treating Kompany, rather than commit to a fixed timetable.
The possibility of him returning to the touchline against Köln has also been raised, although the immediate discussion centres on when he might be able to resume duties at the training ground.
Kompany has been absent from the dugout since the incident, with assistant coach Aaron Danks taking responsibility for the first team. Danks has overseen the side during the Belgian's recovery and has sought to maintain the standards and methods established by the head coach.
Reflecting on his spell in charge, Danks said: "We got through the period and did it with Vinnie's way of leading. Everything he has developed in us, we tried to show."
The Englishman has repeatedly stressed that the squad and coaching staff have drawn on the work they have done with Kompany over the past two and a half years.
Bayern have continued their campaign under Danks, but the club's priority is ensuring that Kompany makes a full recovery before returning to the demands of the job.
The international break offers a natural opportunity to assess his progress, with the match against Köln a potential milestone. However, no decision has been made, and the medical team's clearance will determine when the head coach is ready to return.