Coutinho is heavily rumoured to be on the radar of Barcelona, who are reportedly looking for a marquee signing to replace the departed Neymar.
Reds manager Jurgen Klopp has named a 22-man squad for the first leg of the tie, which takes place at the Rhein-Neckar-Arena on Tuesday night, with Coutinho the most notable omission.
The 25-year-old Brazilian, who arrived at Anfield from Inter Milan in 2013, missed the Premier League draw with Watford on Saturday with a back injury.
According to UEFA rules, Coutinho would not be cup-tied for the rest of the Champions League if he plays in either of the games against Hoffenheim.
Liverpool’s 22-man squad travelling to Hoffenheim:
Alexander-Arnold, Moreno, Lovren, Milner, Wijnaldum, Henderson, Can, Mane, Salah, Firmino, Kent, Solanke, Origi, Gomez, Klavan, Flanagan, Robertson, Matip, Grujic, Mignolet, Karius, Ward