The Switzerland star made just 10 starts in the Bundesliga for Bayern last season, though he still netted six goals and went on to become the standout performer for his country at the World Cup.
Liverpool had expressed interest in paying up to £15 million for Shaqiri during talks with Bayern this summer, with with Serie A giants Juventus and Roma also rumoured to be considering a bid for the 22-year-old.
But Rummenigge told the club's official website: "We've had several enquiries from teams in England and Italy. I've never had a conversation because we are convinced he will have a good career with us. He must stay healthy [but] the coach is convinced by him."
Bayern have agreed a deal to sign goalkeeper Pepe Reina from Liverpool but Rummenigge suggested that there would not be many more arrivals this summer.
"We have a good team. Pep wants 18 top players and five or six talents. He is very happy with his squad, he does not want unhappy players sitting in the stands," the chairman explained.
Borussia Dortmund became incensed by Rummenigge's public talk of Marco Reus's buyout clause after the winger was linked with a switch to the Allianz Arena but the 58-year-old believes that the two clubs retain a large amount of respect for each other, as proven by the mentality within Germany's World Cup-winning squad.
"A friendship seems to have sprung up between the players at the World Cup. This is a good thing," he added. "We are competitors - both clubs want to fight for the championship - but we have respect for each other, no question."