The move should pour around €80 million into the club's coffers, and has already been approved by the boards of both firms. All that remains is for the deal to be signed – and this should take place in the next few days, the magazine says.
And side deals between Audi and FC Bayer's other sponsors such as Adidas or Telekom.
The magazine also suggests that Audi's owner Volkswagen would get a further seat on the FC Bayern board. Martin Winterkorn already sits on the club's board, and could be joined by Audi head Rupert Stadler.
Bayern is currently ranked fifth in the Bundesliga, behind Bayer Leverkusen, Hamburg, Werder Bremen and Schalke 04. Bayern is scheduled to play VfB Stuttgart on Saturday afternoon.