Bayern, who became the first German club to win the treble, with the domestic league and Cup double as well as the Champions League, posted their best financial results in 112 years for 2011/12 with a then record turnover of 332.2 million.
"The treble was a milestone on a sporting level but our turnover (for 2012/13) will also be a new record," he told Sport Bild magazine. "We have broken past 400 million euros for the first time."
Spanish giants Real Madrid and Barcelona are the world's richest club's by income. Real's revenues exceeded 500 million euros for a second consecutive season in 2012-13, rising 1.3 percent to 520.9 million, the club said last month.
Barca said this week income for last season was just over 490 million euros and was projected to rise to 509 million in 2013-14.
Bayern also saw a sharp rise in merchandising sales triggered by their success last season, Rummenigge said.
"We sold for the first time more than a million shirts. In the past I never believed this was possible for a German club."
Bayern, who have reached the Champions League final three times in the last four editions, will announce their financial results next month.
They are top of the Bundesliga and also lead their Champions League group after two wins in two games. ($1 = 0.7355 euros)
(Reporting by Karolos Grohmann, editing by Justin Palmer)
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