The Bavarians' chairman is adamant that reports linking them with the Brazilian are wide of the mark and wants to keep Mario Mandzukic despite Robert Lewandowski's signing
Goal understands that Barcelona have made a renewed enquiry for the Brazilian but reports had also credited the Bundesliga leaders with an interest, among other players.
Rummenigge, however, told the club's official website: "There's a lot of speculation at the moment, especially in England. We're being linked with David Luiz and a number of Spanish players.
"All I can say, very clearly, is that bringing in these players is not of interest to us. We're not concerned about players we're being linked with joining next summer.
"There's nothing lined up, so we have nothing to hide. It's simply not an issue."
Despite the confirmation that Robert Lewandowski will join Die Roten from Borussia Dortmund in the summer, meanwhile, the Bayern chief says that there is still a place at the Allianz Arena for Mario Mandzukic.
The Croatia international has scored 10 Bundesliga goals this season but the recruitment of the Pole has prompted talk of him being moved on.
"We're very pleased with Mario," Rummenigge declared. "He made a significant contribution to us winning so many trophies last year.
"He's a great player who is thriving at Bayern. He has a contract with us until June 30, 2016, and I told his agent during the Club World Cup that we're willing to consider an early contract extension.
"It is by no means a topic of discussion that we want to sell Mario."