The Bundesliga champions' president has fuelled speculation the Poland international will move to the Allianz Arena, while revealing Luiz Gustavo will be allowed to leave
The Borussia Dortmund man looked set to move to the Allianz Arena this summer, but with Jurgen Klopp standing firm and insisting the Poland international sees out the remainder of his contract at Signal Iduna Park, any move is curently on hold.
But Rummenigge has now admitted the striker could partner Mandzukic at Bayern further down the line, after confirming the Croatia international will not be leaving the club.
"Mario Manduzkic is a very important player for Bayern Munich," he told Sport1. "We are very satisfied with his attitude and work rate for the team.
"Perhaps in the future they [Mandzukic and Lewandowski] may even play together."
The 57-year-old Germany legend also believes Pep Guardiola can handle the pressure of coaching the Bundesliga giants.
"At Bayern, the coach always has pressure on him," he continued. "Maybe the pressure on Pep Guardiola is even bigger than usual, but I do not feel he will a problem dealing with it."
Finally, Rummenigge spoke about the size of Bayern's squad - which contains 18 full internationals - and says only Luiz Gustavo will be allowed to depart.
"Luiz Gustavo is the only player we are willing to get rid of," he added.
"Other than him we will not sell any other players. We are playing in the Bundesliga, Champions League and Club World Cup, so we need a big squad."
Bayern open their Bundesliga campaign on Friday evening against Borussia Monchengladbach at the Allianz Arena, as they look to build upon their historic, treble-winning campaign under Jupp Heynckes last season.