"We have already had between 80,000 to 140,000 orders for each of the 16 games," said Bayern board director and former UBS Germany chief, Jan-Christian Dreesen.
"Only for the game against Hoffenheim there are only 68,000 orders and a few remaining tickets available."
The run on tickets for the matches at the 69,000-capacity Allianz Arena comes only five days after the official end of the season and nine weeks before the start of the new campaign in August.
Bayern, who can again expect around 1.2 million fans in total, have just enjoyed their most successful season after also winning the German league and Cup titles.
Bayern had sold out all 17 home games last year by July 11.
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