Karl-Heinz Rummenigge has said he was surprised to be told that Pep Guardiola does not intend to make any more big signings for Manchester City this summer because of the inflated transfer market.
Premier League champions City have had a relatively quiet window so far, bringing in Riyad Mahez from Leicester for a club-record fee and Philippe Sandler from Dutch club Zwolle.
"He [Guardiola] said they originally planned to buy a few more players but decided against it because they no longer want to be part of the madness," Rummenigge said.
"I was a bit surprised to hear this at first, but then I thought it would indeed be wonderful if this statement were to be true until the English window closes.
"City, PSG [Paris Saint-Germain] -- they've always been the global inflaters. Not Real [Madrid], who have spent next to nothing in the past years, which is proof you don't have to join the madness to win the Champions League.
"That's also our path. It's our goal to again lift the Champions League trophy, rather sooner than later."
Rummenigge said Bayern want to "use Robert Lewandowski as a warning and make sure, both internally, and externally it is known Bayern Munich are club which ticks completely differently" as far as the transfer market is concerned
In May, Poland striker Lewandowski said he wanted to leave after eight years to seek a new challenge, with agent Pini Zahavi saying "money or a specific club" were not the motivation.
"We wanted to show the door remains closed," Rummenigge said. "He wanted to leave, but we informed him that we won't do it. We are totally happy with the player.
"It's not in our interest he leaves, no matter if someone puts €100 million to €150m on the table."
Speaking to Sport Bild, the Bayern chief later said: "I predict today: Lewandowski will play a great season and better his record of 30 league goals for Bayern Munich. I am convinced of that. He will step on the gas like never before."