Jurgen Klopp is also without the injured Virgil van Dijk, Joe Gomez, Alex Oxlade-Chamberlain, Naby Keita, Xherdan Shaqiri, Trent Alexander-Arnold and James Milner.
Liverpool said Alisson missed out as a precaution due to a tight leg muscle.
Kelleher, 22, has only played three times for the Reds with all his previous appearances in the FA and League Cup.
However, he has been handed his chance ahead of Adrian, who was in goal for a humiliating 7-2 defeat by Aston Villa in September.
Liverpool lead Champions League Group D by two points from Ajax and Atalanta and need just two more points from their final two games in the section to reach the last 16.