The 23-year-old German international came off for Gabriel Jesus following an innocuous first-half incident where Sane appeared to get his studs stuck in the Wembley Stadium pitch.
Sane's removal and subsequent substitution came seconds before former Liverpool standout Raheem Sterling opened the scoring for the domestic treble winners.
Bayern have made no secrets about their desire to lure Sane to the Allianz Arena, with manager Niko Kovac admitting discussions between the relevant parties were underway. "I'm confident and assume that we will get him," Kovac said days before calling City boss Pep Guardiola to apologize about his public statements of interest.
The Bundesliga holders then backtracked with a statement on Twitter that read, "News reports made today stating that Leroy Sane has decided to join FC Bayern do not correspond to the facts."
Sane has two years remaining on his current terms with City.