Multiple reports in England and Germany have reported that Sane will join Bayern in a deal worth £44.5m.
The Germany international has flown to his homeland to undergo a medical and complete the move.
The deal also includes £10m in add-ons, with City inserting a 10 percent sell-on clause.
The news concludes a drawn-out saga which saw Sane reject a contract extension to force through a return to the Bundesliga.
The 24-year-old was set to become a free agent next summer, leaving City happy to recoup some sort of fee.