The move could mean long-term Liverpool target Ilkay Gundogan is now free to leave the German giants.
Gundogan joined Dortmund in May 2011 and Calciomercato claim he's a target for Reds boss Jurgen Klopp and Juventus.
The arrival of Torres at the Westfalenstadion is the biggest indication yet that the Germany international’s Bundesliga future is in doubt.
Speaking earlier this month, Gundogan admitted he was considering his options.
He told Bild: "There is still no decision, and of course, everything has to be considered very carefully, because your career is limited in time.
"I know what I have at my club, and I'm not going to lose sight of it.
"But again, a decision is definitely not made."
The midfield ace has made 146 appearances for Thomas Tuchel's side, scoring 16 goals.
Klopp has already snapped up Marko Grujic and young Polish goalkeeper Kamil Grabara.
The Anfield outfit also secured a surprise loan deal for England international Steven Caulker from QPR.
