The Turkey international's career has stuttered since he left the German champions in 2011 for Real Madrid, but BVB are interested in bringing him back to Signal Iduna Park
The Turkey international joined los Blancos after lifting the Bundesliga title with Dortmund, but struggled to establish himself in Jose Mourinho's team.
He moved to Anfield on loan at the start of this season, but after showing early promise he has since found his playing time limited, dropping behind Jordan Henderson in the Reds' pecking order.
Now the reigning German champions are pursuing the possibility of bringing Sahin back to Dortmund, the place where he began his career.
"Nuri is one of ours and we're closely monitoring his situation," Dortmund director Michael Zorc told Bild.
"The problem in Liverpool is he is not playing in his best position.
"We have previously said that we might make a move if he says he only wants to play at Dortmund. We have to remain realistic, though. Nothing has changed in that regard."
Sahin has started just seven league matches for Liverpool, leading to speculation that Brendan Rodgers could pull the plug on Sahin's stay at Anfield in January.