However, Bayern are aware of a release clause, believed to be in region of £20m, in the 25-year-old's contract and Rummenigge has revealed that they could be tempted to trigger it to land the Germany midfielder.
"We know what quality he has and we also know what clause he has," he told Sport1.
"A young, Germany international with such quality is probably interesting for us, but I don't want to cause any ill-feeling with Dortmund."
He added: "Of course our relationship with Dortmund is not good. Borussia Dortmund have informed us that they don't see any point in eating together with Bayern Munich."
Reus, who has scored 49 goals in 89 Bundesliga and Champions League games for Dortmund, is expected to be one of the hottest transfer properties of 2015, with Arsenal, Liverpool and Real Madrid all admirers.