The Daily Star says Gundogan had been lined up by Arsene Wenger before they snapped up Mesut Ozil.
But now United want him to transform their midfield.
Gundogan, 22, is under contract at Dortmund until 2015 but is refusing to sign a new deal.
The Red Devils wanted Gundogan back in 2011 and he declared Manchester United were "his dream club".
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball