The 17-year-old attacking midfielder burst onto the scene in the back end of last season, becoming both Bayern's youngest player and goalscorer in the Bundesliga.
England Under-21s international Musiala has made 19 appearances for the Bavarian giants overall, but his current deal expires next year and fresh terms have yet to be agreed.
Goal claims that, with Bayern unwilling to match the youngster's £100,000-a-week wage demands, he may be on his way to the Premier League in the summer.
Reigning English champions Liverpool, plus Manchester rivals United and City, are all said to be closely monitoring the situation.
Musiala's camp are said to be confident that one of the Premier League big boys will match the six-figure weekly sum the attacker is after, feeling that he has already proved his worth over the past seven months.