The Belgium international, who has two years to run on his contract, is expected to leave Anfield before the European transfer window shuts on August 31.
BVB have registered their interest but have yet to table an offer for the 23-year-old frontman.
Dortmund boss Lucien Favre is desperate to bolster his strikeforce. After selling Pierre Emerick Aubameyang to Arsenal back in January, they signed Chelsea's Michy Batshuayi on loan but he has since left and will spend the 2018/19 campaign with Valencia.
Jurgen Klopp is prepared to sanction the sale of Origi to his former club but the Reds are adamant his exit will be on their terms and they are prepared to hold out for what they want.