According to Bild, the attacking midfielder took part in training at Sabener Strasse for the first time since being sidelined, marking an important step in his recovery.
Musiala's return will be welcomed by Bayern, who have missed his creativity and ability to make things happen in the final third. His close control, dribbling and vision make him one of the team's most dangerous attacking players.
However, his return to training does not mean he is immediately ready for competitive action. Bayern are expected to manage his workload carefully as he builds up his fitness following the lengthy absence.
The German international's availability will be particularly important with a demanding schedule ahead, although the club will not want to risk a premature return.
Bayern's next Bundesliga fixture is away against Mainz on Saturday, but it remains to be seen whether Musiala will be ready to feature.