The attacking midfielder has recently been linked with Liverpool, Manchester City and Chelsea.
The 21-year-old's contract with Bayern expires in the summer of 2026. But Musiala has put off plans to discuss a new deal.
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Eberl now emphasises that Musiala is untouchable.
"Yes! He is supposed to be the face of FC Bayern in the future," says Eberl to Sky Deutschland.
"Jamal is a player who gives extremely great joy. He embodies FC Bayern extremely well. It is our intention to make him the new face of FC Bayern."