The Japan international's future has come into question after failing to secure a regular starting spot in the first team under manager David Moyes this season.
"I have seen just how good de Bruyne is, and at Dortmund we have seen how well Kagawa can do," Bild quotes Aloffs as saying.
"If such players are possible, you of course think about them, but we should not raise the hopes of our fans. In the end they comment, 'once again, you failed to sign him'."
Kagawa moved to Old Trafford last year for a reported £12m.