Coutinho also missed Liverpool's 3-3 draw at Watford on Saturday due to a back injury, with manager Juergen Klopp conceding he had no control over the 25-year-old's future at the club.
Under current UEFA rules, Coutinho's participation in the play-off round against Hoffenheim would not jeopardise a move in the current transfer window. The Brazil international will remain eligible to feature for another club in next month's Champions League group-stage.
The Merseyside club will also be without striker Daniel Sturridge, who has failed to recover from a thigh injury sustained during the pre-season.
Hoffenheim host Liverpool at the Rhein-Neckar-Arena on Tuesday before the two sides meet again at Anfield next week.
(Reporting by Hardik Vyas in Bengaluru; Editing by Gareth Jones)
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