Die Roten are unbeaten after their first eight league games – opening a sizable lead over rivals Borussia Dortmund – but they must not get complacent, says their former striker
The Bavarians opened up a 12-point advantage over defending champions Borussia Dortmund, after Jurgen Klopp's side slipped to a 2-1 defeat by Schalke, whilst last year's Champions League finalists strolled past Fortuna Dusseldorf 5-0.
"We have had a great start to the season, whilst Dortmund haven't had the best of starts," Rummenigge told the Fifa website.
He added: "We have set a new record with eight wins in a row, but we won't be celebrating with champagne yet."
Dortmund recovered from a nine-point deficit last season to overcome Bayern, but Thomas Muller believes that Jupp Heynckes' side should turn their attention to Schalke and Eintracht Frankfurt in the battle for the Bundesliga title.
"There are more teams than just Borussia Dortmind," he told Sky Sports. "We can be pleased that we have made such a good start to the season and we have learnt to concentrate only on ourselves. If we carry on playing like this, then it will be hard for any opponents to beat us."