Van Dijk reiterated his desire to leave Southampton after showdown talks with Saints hierarchy.
Both clubs said to be weighing up £12m summer bids for Dutch centre-back.
Manager Mauricio Pellegrino will hold talks with the Netherlands international this week.
Van Dijk is attracting interest from Liverpool, Manchester City and Chelsea.
The Netherlands international is reportedly eager to work under Jurgen Klopp at Anfield.
England Under-17 defender, also linked with Southampton, has signed a three-year contract at Goodison Park.
Van Dijk is training alone as his future at St Mary's remains uncertain.
Dutch defender expected to become a Reds player before the end of the summer transfer window.
Van Dijk has been left out of Southampton's squad for their pre-season trip to France.
Dutch defender is training alone after informing Saints of his desire to leave the club.
Saints boss Mauricio Pellegrino says defender is 'psychologically not 100 per cent.'
Liverpool have only signed two players in the summer transfer window so far.
Nicol says Liverpool will put the team on Keita's back in a couple of years if they sign him.
Arsene Wenger wants Celtic forward Dembele to replace Sanchez if he leaves The Emirates Stadium.
Virgil van Dijk has been among Southampton's best players.
Austrian defender seeking to increase exposure to regular first-team football.
Reds had ended interest in Van Dijk after being reported for illegal approach.
La Liga giants say they may have to accept PSG's decision not to sell the Italian.
The Portugal international is reportedly a candidate to replace Kyle Walker at Spurs.
Liverpool legend Steve Nicol does not believe the Southampton defender is worth £60m ($76.9m).
Argentine succeeds the unpopular Claude Puel, who was dismissed after just one season in charge.
Chelsea midfielder and Southampton forward were both substituted early during Thursday's 3-0 win over Poland.