The German international has made 24 appearances for Dortmund this season in all competitions, and his performances have drawn the attention of many high profile European sides, namely Champions League finalists Juventus.
According to the report by TMW, interim manager Guus Hiddink would have to pay €17 million for the former SC Freiburg man.
The news comes following the announcement that Gary Cahill wants to leave Stamford Bridge after losing his place to John Terry and Kurt Zouma. Liverpool are reportedly plotting a move for the English defender according to the Daily Mirror.
Ginter moved to Dortmund in July 2014 from SC. Freiburg, for a fee, believed to be in the region of £8m. He has made 44 appearances for his current side, scoring on three occasions. He has also created goals for his teammates, being the provider 10 times, in all competitions this season. This season, Dortmund have only lost a single league game in which he has played.
Ginter, 22, could bring a lot to Chelsea or Juventus. This season, he has featured as a defensive midfielder as well as a right-sided defender and a right-back. But on a whole, his preferred position is as a central defender.