The 19-year-old has been in impressive form for the German giants during the 2022-23 campaign, scoring 12 goals and registering 10 assists in 22 appearances in all competitions.
Musiala represented Germany at the 2022 World Cup, meanwhile, and he was arguably one of only a few DFB-Team players to emerge from the tournament with credit.
The teenager's current deal at Allianz Arena is due to run until June 2026, but it is understood that Bayern will sit down with him in the near future to discuss improved terms.
According to Fichajes, there are 'many interested clubs', with Man United and Real Madrid two teams closely monitoring the teenager's development.
Bayern CEO Oliver Kahn recently branded Musiala "an important cornerstone in the future of FC Bayern".
"Jamal has enormous qualities that he's showing consistently at a high level at 19. He's also very ambitious and always wants to improve. We're glad we have him. Jamal will be an important cornerstone in the future of FC Bayern," he told Bild.
Meanwhile, during an interview with the same publication, Bayern sporting director Hasan Salihamidzic said: "Jamal was one of Germany's bright spots at the World Cup. Watching him play is simply fun.
"Playing at a World Cup was a valuable experience for him. Although the elimination is bitter, Jamal is 19 and still has many tournaments to play for Germany.
"We saw that he could transfer his performances at Bayern to the national team. We at Bayern will do everything to continue supporting him in his development."
Musiala spent time with Southampton and Chelsea during his youth career before making the move to Bayern in 2019, and he debuted for the German giants in 2020.
The attacker will not turn 20 until the end of February, but he has already made 100 appearances for his German club, scoring 27 goals and contributing 17 assists in the process.
Liverpool and Manchester City have also been credited with an interest in the teenager, who recently refused to rule out a future move to the Premier League.
"Playing [my] whole career at FC Bayern? Many factors come together," Italian journalist Fabrizio Romano quoted the youngster as saying. "I'm very happy at Bayern. You never know what will happen in six to seven years.
"Premier League? Really strong league, big stars go there. But... no idea, now I'm at Bayern. [It's a] super top club."
Musiala has nine goals and seven assists in 14 Bundesliga appearances this term, while he provided two assists in five outings in the group stage of the Champions League.