The Reds were heavily linked with a move to sign the Netherlands international earlier this summer but a deal has failed to materialise so far.
Indeed, Liverpool issue a statement apologising to Southampton for pursing Van Dijk last month, adding that they were ending their interest in the former Celtic man.
However, transfer speculation has continued to link Liverpool with a big-money deal to sign the Southampton star before the start of the 2017-18 season.
RB Leipzig midfielder Naby Keita is rumoured to be another of Klopp’s top targets and Liverpool reportedly failed with a club-record offer last week.
However, the Reds are being linked with a fresh approach to sign the versatile 22-year-old midfielder after his impressive debut season in Bundesliga.
Journalist Marcotti believes Southampton and RB Leipzig will find it difficult to keep Keita and Van Dijk if both players have their hearts set on a move to Liverpool.
“Liverpool are playing a waiting game,” Marcotti told ESPN FC on Monday.
“They have to be careful with Virgil van Dijk. Leipzig and Southampton can say whatever they want to say about not wanting to sell.
“The reality is it is extremely difficult to keep an unhappy player. That’s why players force moves.”
Liverpool signed seven players in the summer transfer window last year.
Klopp led the Reds to a fourth-place finish in his first full season in charge at Anfield.
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