The Sun is reporting that Van Dijk is prepared to force through a move to the Merseyside outfit this summer.
The same article states that the Netherlands international is only interested in a move to Anfield despite being previously linked with Arsenal, Chelsea and Manchester City.
According to the story, Van Dijk, 26, remains Liverpool’s number one target despite the Reds being linked with a move to sign RB Leipzig midfielder Naby Keita.
Liverpool were heavily linked with a move to sign Van Dijk earlier this summer but pulled out of the race to sign the former Celtic star.
Indeed, the Reds issued an embarrassing statement ending their interest in the Dutch defender and apologising to Southampton over their pursuit of the centre-half.
Liverpool finished in fourth place in the Premier League table in their first full season under Klopp.
The Reds are still waiting to win their first trophy under Klopp after his appointment as Brendan Rodgers’ successor in October 2015.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news