Dortmund confirmed in a statement that the 27-year-old Germany international, who is under contract till June 2017, had submitted an official transfer request.
"Defender Mats Hummels Borussia Dortmund has communicated his desire to leave the club in the summer and wants to join league rivals Bayern Munich next season," Dortmund said on their website.
"So far, Bayern Munich has not made an offer. As a precaution, it is pointed out that... no exit clause has been agreed and the player is logically tied to Borussia Dortmund until June 30, 2017."
A switch to Bayern would represent something of a homecoming for Hummels, who came through the ranks at the Bavarian club before moving to Dortmund in October 2008.
Dortmund are currently second in the Bundesliga table, trailing Bayern by seven points.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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