The 23-year-old won his first caps for Germany last year and his form for Freiburg has led to widespread interest.
Lucien Favre plans to use three at the back next season, but considers only Mats Hummels and Dan-Axel Zagadou viable for that system.
Due to the Coronavirus, BVB have put their transfer business on hold for the time being until the financial impact is known.
However, if a defender leaves Dortmund in the summer, things could happen quickly. And the man BVB will target is Koch.
Koch is out of contract at Freiburg in 2021 and has already signaled that he will not extend it.
As a result, Freiburg want to collect a transfer fee for the young centre-back. A figure of €10m is under discussion at the Schwarzwald-Stadion.
Koch, who can also play as a defensive midfielder, has made 27 Bundesliga starts for Freiburg this season.