According to ESPN, the Bundesliga champions want to sign the Chilean, whose contract expires at the end of the season.
Sanchez is highly unlikely to sign a new deal at the Emirates, and is seeking pastures new ahead of next season.
The former Barcelona man was in line to join Manchester City in the closing stages of the summer transfer window. However, if reports are to be believed, Arsenal’s failure to land Thomas Lemar saw Sanchez’s proposed £60m move fall through.
Bayern Munich and PSG were two teams cited with strong interest in Sanchez throughout the summer, and the former appear to have revived their desire to sign him.
City are reportedly plotting a January move for Sanchez, with Arsenal in danger of losing their star man for free when the summer comes around.
Sanchez is able to discuss a pre-contract agreement with foreign clubs in the January window, which could work very well in Bayern’s favour should they choose to pursue him.