The 23-year-old is thought to be surplus to requirements at Anfield with his route to the first team blocked by the likes of Roberto Firmino, Mo Salah and Sadio Mane.
The Belgian spent last season on loan in Germany with Wolfsburg and it would seem that he caught the eye of bigger fish in the form of Dortmund.
Dortmund are on the lookout for a new striker having sold Pierre-Emerick Aubameyang to Arsenal in January and seen his temporary replacement, Michy Batshauyi, return to Chelsea following the completion of his loan spell.
Origi has two years left on his contract at Anfield, but the 'Reds' are thought to be open to a sale providing their valuation of the player, thought to be in the region of £27m, is met.