The 50-year-old was released from hospital on Wednesday evening after having admitted himself earlier in the day, missing the first training session of his full squad since their return from international duty.
Liverpool have said Klopp may require further check-ups in the coming days but it is yet to be seen how that will affect his presence at the club’s Melwood training ground.
The club issued a statement on Wednesday afternoon, just as the team were due to begin training, in which they confirmed Klopp’s absence.
“There are currently no plans for Jurgen to remain in hospital beyond his appointment and he will therefore return home; however, he may require further check-ups in the coming days,” said the statement.
“The club urges that the privacy of Jurgen, his family and other patients is respected while attending hospital visits.”
In February 2016 Klopp, who last week made a trip to South Africa for a charity event, missed the 2-2 draw at home to Sunderland after being hospitalised after suffering appendicitis.
On that occasion assistants Peter Krawietz and Zelko Buvac oversaw the team’s 2-2 draw and they, plus coach Pepijn Lijnders, took Wednesday’s training in the manager’s absence.
Players joining the session after international duty included Philippe Coutinho and Roberto Firmino, who both played for Brazil against England at Wembley, Simon Mignolet (Belgium) and Joe Gomez, Dominic Solanke and Trent Alexander-Arnold – who represented England at senior and under-21 level – and Wales duo Ben Woodburn and Danny Ward.
Senegal’s Sadio Mane, who came back on Tuesday after complaining of another problem with his hamstring while on international duty, has not yet been ruled out for the weekend.