The England Under-21s international has recently been linked with a move to the Premier League after entering the final 18 months of his contract at the Allianz Arena.
Rather than lose the attacking midfielder for free at the end of next season, Bayern were said to be looking to cash in this summer if fresh terms could not be agreed.
However, Goal claims that talks between the Bavarian giants and Musiala are progressing well and he is now expected to put pen to paper on a new long-term deal.
Musiala, also touted as a possible target for Manchester City, burst onto the scene last season when becoming both Bayern's youngest player and goalscorer in the Bundesliga.
The 17-year-old has played 21 times in all competitions this term, scoring three times.