The 27-year-old has been left out of the Leipzig squad for Sunday's Bundesliga match at fellow Champions League side Wolfsburg.
Bayern are expected to pay 16 million euros ($19 million) for the Austria midfielder and German daily Bild say the clubs are in discussions.
Sabitzer, who has scored 52 goals in 229 appearances for Leipzig since 2014, is out of contract next June.
He looks set join Julian Nageslmann, who quit Leipzig to coach Bayern this season, and former team-mate Dayot Upmecano, who also switched to Munich from Saxony for this season.
The transfer window closes on Tuesday and Bayern sports director Hasan Salihamidzic did not deny interest in Sabitzer before Saturday's Bundesliga match at home to Hertha Berlin.
Salihamidzic however dismissed reports Bayern want to sign Jonas Hofmann and Matthias Ginter from Moenchengladbach before Tuesday's deadline.
