Wagner worked at BVB as reserves coach.
The Sun says taking Huddersfield into the Premier League has impressed his old club.
They have struggled this year under Peter Bosz and have crashed out of the Champions League after failing to get out of Tottenham's group.
Wagner is expected to be in the frame if there is a change of coach at Dortmund.
He signed a new two-year deal in the summer following promotion from the Championship.