The German missed his side's 2-2 draw at home to Sunderland on Saturday as surgery was planned for him in the afternoon at a Liverpool hospital.
Reorts said he was eager to resume his normal duties at the club's training ground.
He could even address the media at a scheduled press conference to preview Liverpool's FA Cup fourth round replay at West Ham on Tuesday.
A decision will be made later in the day as to whether the 48-year-old will be allowed to be back at his desk.