Wolfgang Holzhauser, Rummenigge's opposite number at Leverkusen, is unhappy that Bayern manager Jupp Heynckes sent a text message to Bender after he scored for Germany at Euro 2012.
Holzhauser told Bild: "I am very surprised to see Jupp Heynckes being able to text an SMS by now."
The Bayern chief has rejected Holzhauser's remarks, but conceded that the club are interested in players similar to the 23-year-old German.
"I recommend that Leverkusen take things in a more relaxed and more confident manner than right now," Rummenigge said.
"Everyone knows that we are watching the transfer market for players in that position (defensive midfielder) and our sports directors have some players on their list who they are watching.
"I can only say that we are pretty relaxed in this case. We could imagine that Lars Bender will be a target for Bayern Munich, but we have to wait.
"We know that there is a price for every player and if Bayern Munich is willing to pay that price, it is possible that the player will pull on a Bayern shirt but we have to calm down."