ESPN FC can now reveal that Bayern did indeed make a very significant offer -- not once, but twice. Rummenigge bid 31 million euros at the beginning of the summer, and both Dortmund and Lewandowski were officially told that the offer was still valid a couple of months later. Bayern were pushing but with time on their side, they didn't try a third time.
All of this still begs the question why Dortmund didn't simply cash in. Defiance in the face of Bayern's raid on their team was certainly a factor, as was sending a message: Dortmund did not want to be seen as a selling club. But there were more pragmatic reasons as well.
First, they hoped Lewandowski could still be sold abroad. There was a precedent: in 2011, Leverkusen's refusal to let Arturo Vidal move to Bayern had resulted in Juventus hijacking the deal and the player changing his mind. Dortmund must have felt that the Pole and his agents could be swayed in a similar manner. They thought: Why wait another year for Bayern -- and a big pay rise -- instead of moving to Spain or England immediately? But with Lewandowski and his camp not entering any negotiations with clubs other than Bayern, Dortmund made a decision that he'd be kept on for another year regardless.