Dortmund aim to replace Mkhitaryan who signed for Manchester United today with the Turkish international winger.
Turan would join international teammates Nuri Sahin and Emre Mor if he were to make the move to the German giants.
There is controversy over the future of Turan at Barcelona with reported from Spain suggesting the club are open to offers if the price is right.
Turan did only sign for Barcelona last summer on a big money five-year deal but missed the first-half of the season due to the FIFA transfer ban imposed on the club.
Barcelona president Josep Bartomeu did however, hint that he was happy with Turan’s first season in contrary to reports claiming that the board were unhappy with his performances last season.
The club president said: “The coaching staff count on Arda Turan and we thank both him and Aleix [Vidal] for the patience they showed to go six months without being able to play. As for the sporting section, I’d give them a nine out of 10 because four trophies in one season isn’t bad at all”.
Turan would play in the Bundesliga for the first time in his career if he were to make the move this summer.