The Bayern Munich CEO has hinted that the Croat could leave the Allianz Arena this summer and admits that he reacted angrily to BVB's criticism this year
Pep Guardiola left the former Wolfsburg man out of his 18-man squad for Saturday's DFB-Pokal final date with Borussia Dortmund, allegedly for disciplinary reasons.
Bayern will sign Lewandowski from BVB in the summer and Rummenigge believes Mandzukic might not want the extra competition.
"If Mario stays here, it won't be easy for him," he told FAZ.
"Because a world-class player is coming to us. The question is whether he wants to face up to this competition or would prefer to go to another club.
"We are open and fair and we talk about everything, so nothing is decided."
Bayern have been in a war of words with Dortmund, who are unhappy that the Bavarians have signed two of their star players in consecutive years following Mario Gotze's arrival at the Allianz Arena last summer.
Rummenigee has accepted that he did not deal with the situation well but admits that BVB's approach can annoy him at times.
"When I have personally been critical of Borussia Dortmund, it's only because I did not like it when they tried to present us as a Goliath, who runs the Bundesliga like a robber baron.
"On the other hand, I should have had a bit more restraint."