Reports have suggested that the Borussia Dortmund attacking midfielder could be available for as little as £20m at the end of the season due to a clause in his contract, and Rummenigge has admitted that Bayern are keeping an eye on the 25-year-old's situation.
"If a German international has an exit clause and his contract is running out, Bayern is obliged to think about him," Rummenigge told Sport 1. "With Marco Reus, his release clause is known.
"Whether we deal with it, I cannot seriously predict. We've talked too little internally about the subject. There are many great clubs from other countries who would be interested in signing Marco Reus.
"Of course they will try to extend his contract. But at the end of the day the player will decide what he wants."
Despite the clause in his contract, Reus still has three years remaining on his current deal.