The Reds boss is reported to have made the club’s doctors aware of feeling unwell overnight and consequently visited a medical facility on Merseyside.
Liverpool added that Klopp is not due to remain in hospital, but further checks on his condition may be required.
A statement on the club’s official website read: “Jurgen Klopp has attended a hospital appointment today [Wednesday] as a precautionary measure, after feeling ill.
“He is being assessed by doctors and will be absent from training on Wednesday as a result.
“There are currently no plans for Jurgen to remain in hospital beyond his appointment and he will therefore return home this evening; however, he may require further check-ups in the coming days.
“The club urges that the privacy of Jurgen, his family and other patients is respected while attending hospital visits.”
Liverpool return to Premier League action following the international break against Southampton at Anfield on Saturday.