The Japan international has struggled with Manchester United since his June 2012 move from Signal Iduna Park with his Old Trafford shortcomings prompting rumours of a Dortmund return.
Hummels spoke of the possibility of Kagawa heading back to BVB this summer and said it would be of great benefit to the current Bundesliga runners-up.
"We would take him with open arms, of course," Hummels told Kicker.
"Having an offensive line with [Marco] Reus, [Henrikh] Mkhitaryan and Kagawa would certainly be stylish.
"But I would not say anything about the other great players we have playing for us. The attacking midfield is probably the best part of our team without Shinji."
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