The Colombian attacking midfielder is approaching the end of a two-year loan spell from Real Madrid.
Though his time in Bavaria has been a struggle, with injuries having largely hampered his progress, the top brass of the club seem intent on keeping him.
“I am firmly convinced that James Rodriguez will play for Bayern next season,” Rummenigge said.
“I am sure that (coach) Niko Kovac values his quality.
“I do not believe that there is any problem between the two,” he stated.
Rummenigge was full of praise of Rodriguez, revealing his admiration for the Colombian’s style of play.
“I am a massive fan of James.
“He has a great left foot and, for me, is a superstar and we must choose the option (to sign the player) that we have until 15 June,” he added.