"Of course, I know that the public is dreaming of the treble, but we also know well enough how difficult and unpredictable the Champions League is," Rummenigge wrote in the programme for Friday's season opener against Werder Bremen.
"Even perfect football, even being the best team in Europe, they are no guarantees for winning this title. "The Champions League is a marathon."
Under new coach Carlo Ancelotti, Bayern will kick off the 2016/17 season against Bremen with a sell-out crowd of around 75,000 expected at the Allianz Arena as the defending champions begin their bid for a fifth straight league title.
The Bavarian giants made history last season under Ancelotti's predecessor Pep Guardiola by becoming the first German club to win the league title four years in a row. They then completed the domestic double by also winning the German Cup.
But the Champions League is the trophy Bayern fans crave the most and they will be dreaming of a repeat of their treble-winning 2012/13 campaign under Jupp Heynckes.
Bayern, who have won the European Cup five times, have drawn Eindhoven, Russian club Rostov and Atletico Madrid, who knocked them out of last season's semi-finals, in Group D.
"It's a demanding group and in Atletico Madrid, we have a very strong opponent ahead of us," said Rummenigge following the draw in Monaco.
"We haven't played against Eindhoven for a long time and this will be the first time against Rostov.
"We shouldn't underestimate any opponent and Atletico are definitely favourites."
Bayern have reached at least the semifinals of the Champions League in each of the last five seasons, exiting in the semis in each of Guardiola's three seasons in charge.
Winning the Champions League is the icing on the cake for any Bayern season, but winning a 27th German league title this season is Ancelotti's main task.
"Four titles in a row was a milestone, but I think a handful, one after the other, sounds much better," added Rummenigge. "The German league title remains the most honest, the most important.
"Seeing FC Bayern stand on the town hall balcony in May (celebrating winning the league) is a part of Munich as Oktoberfest in the autumn and it's a beautiful tradition we want to keep."
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