Striker Mandzukic, the scorer of 10 Bundesliga goals this season, has been linked with Premier League leaders Arsenal in recent days, with Arsene Wenger apparently keen to boost his injury-hit forward line.
However, Rummenigge has moved quickly to quash such speculation a matter of hours after Bayern confirmed that forward Robert Lewandowski will join from Borussia Dortmund at the end of the season.
Bayern's interest in Lewandowski had led to suggestions of Mandzukic leaving, but the club are keen to discuss a new deal with the latter, who joined from Wolfsburg in June 2012.
"We're very pleased with Mario," Rummenigge told the club's official website.
"He made a significant contribution to us winning so many trophies last year.
"He's a magnificent player who has come on superbly at Bayern. He has a contract with us until 30 June 2016, and I told his agent that we're certainly prepared to consider extending his contract well before it expires.
"We have absolutely no intention of letting Mario go."
Chelsea defender Luiz, meanwhile, has reportedly emerged as a target for Bayern and Barcelona, but the German and European champions are not interested in the 26-year-old Brazil international, according to Rummenigge.
He added: "There's a lot of speculation at the moment and it’s an extreme situation in England.
"We're being linked with David Luiz and other Spanish players at the present time.
"Let me state this very clearly: it’s all of no interest whatsoever to us. We're not yet concerned about the situation regarding the playing staff next summer.
"There's nothing lined up, so we have nothing to hide."
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