Kagawa has endured a difficult second season at United, with the Japanese international having only started 12 games in the Premier League this campaign.
"We would take him with open arms, of course," the defender told German sports magazine 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."
Kagawa has scored six goals in 54 appearances for United since joining from Dortmund in the summer of 2012.