The Bundesliga champions have reportedly set their sights on the Turkish striker, who is in great demand after an impressive season at the Huseyin Avni Aker Stadium
The 26-year-old striker has emerged as one of most sought-after players in Europe after scoring an impressive 35 goals in all competitions this season.
Dortmund coach Jurgen Klopp is eager to fine-tune his squad in the summer transfer window, with the acquisition of a quality striker reportedly a priority for the Bundesliga champions.
It is believed that Yilmaz, who has a contract with Trabzonspor until 2015, could arrived at the Westfalenstadion in a deal worth €5 million.
Questioned about Dortmund's interest in the Turkey international, Klopp said: "I know Yilmaz, I have heard about him."