The former RB Leipzig star comes off contract at Liverpool in June.
Keita is one of Dortmund's highest priorities for next summer's transfer window as they look to bolster their midfield, says BILD.
Talks over a new deal are ongoing between Keita and Liverpool, however other clubs' interest in the 27-year-old may put discussions on hold.
The midfielder has yet to feature for Jurgen Klopp's side this season due to a hamstring injury, which is the latest in a long list of fitness problems.
Keita has missed 72 games for the Reds over his four full seasons at the club having struggled with ankle, groin and hamstring injuries often.