Jurgen Klopp is keen on signing another goalkeeper for Liverpool, and a top target is available at a bargain price.
The report states he has a release clause in his contract of nine million Euros - equivalent of £6.5 million.
Horn currently plays for FC Koln, who are riding high in seventh in the Bundesliga table, with 18 points from 12 games, just two points off a Champions League qualifying place.
Who is Timo Horn?
Horn is 22-years-old and currently has a contract at Koln until 2019, albeit with a reported release clause.
He came through the club's youth system and has made 120 appearances for the club, keeping 49 clean sheets.
His performances have earned him four caps for Germany's under-21 side, and he is one of a number of challenges for Manuel Neuer's senior position, along with Marc Andre Ter Stegen and Lorus Karius.
Horn was linked with a move to Aston Villa back in May, with The Mail reporting the club's interest.
Horn would be real competition for Liverpool's number one Simon Mignolet, who has not entirely convinced since signing for the Reds back in 2013.