Borussia Dortmund striker Lewandowski signed a five-year deal with Bayern on Saturday after passing a medical in Munich.
The Poland international will join Bayern on a free transfer once his current contract with the Westphalians expires at the end of June, but his arrival does not automatically mean the club's current top-scorer Mandzukic will have to leave.
"We're very happy with Mario," Rummenigge said on his club's website. "He made a major contribution to us winning so many titles last year. I just have to think back to the goal in London.
"He's a fantastic player who has come on leaps and bounds with Bayern.
"His contract runs until 2016 and I told his advisor in Marrakech that we would be willing to talk about an extension. We have absolutely no intention of selling Mario."
Rummenigge also ruled out a move for Chelsea defender David Luiz.
"There's always lots of speculation and it's extreme in England, but I can say for certain that he is not an issue for us," sad Rummenigge.
"I personally hope that Holger Badstuber comes back (from injury). That would be a new arrival who would do Bayern a lot of good.
"He's a great lad and an important player for us."
The Bundesliga leaders on Sunday set off for a 10-day training camp in Doha, where they will prepare for the second half of the season, which starts with a trip to Borussia Monchengladbach on January 24.
Bayern winger Arjen Robben, meanwhile, believes the Bundesliga champions are about to get even better with the arrival of Lewandowski.
"He's a super player, a really good player," the Dutchman told Sport1 television. "He is one of the best strikers in the world.
"It's fantastic that he's coming to us. It makes our squad even stronger."
Without Lewandowski, Bayern won all there was to win in 2013, apart from the German Supercup which was taken by Dortmund prior to the current season.
Robben played a major role in winning the Bundesliga, DFB-Pokal and Champions League treble, scoring the decisive goal at Wembley as Bayern beat Dortmund to Europe's greatest prize in May.
However, he missed the Club World Cup triumph due to injury and is working hard on returning for the second half of the season.
"I've started doing some individual training sessions and we're taking each day as it comes," he said.
"We're taking things easily and trying to increase the workload day by day. Things are moving on and I was able to do some work during my holidays, which is good."
Robben's own contract expires in 2015 and he has stated his desire to stick with the all-conquering club.
"It was the best marriage I ever had in football," said the 29-year-old.
"We haven't spoken about it yet but I'm happy here and the club know what they've got in me."