Bellingham is expected to spark off a major race for his services with some of the biggest clubs in Europe vying for his signature.
Chelsea, Manchester City, Manchester United and Liverpool are vying to take him to England and Real Madrid are interested in adding him to their talented squad at the end of the season as well.
Dortmund are keen to offer him a new contract but are expected to sell if they receive a fee of around €150m for the England midfielder.
And Rummenigge stressed that it is the difference between Dortmund and Bayern Munich that is keeping the Bavarians at the top of German football.
The former Bayern Munich CEO stressed that the Bavarians would not countenance selling Bellingham if he was their player.
Rummenigge told Funke Mediengruppe: “The difference is in the philosophy.
“As a rule, Bayern Munich do not need to sell players in order to improve their balance sheet.
“At Dortmund, there is already talk of Bellingham leaving.
“Bayern would not sell such a player.”
Bellingham has not made a call yet and Dortmund are hopeful that he will sign a new contract soon.
