But the Reds now face a real battle to convince Jurgen Klopp's number one transfer target his next destination should be Anfield.
Van Dijk has long been a priority for Klopp, who has earmarked the 25-year-old centre-back as a player who can instantly improve his defence.
Southampton accept a parting of the ways is inevitable when the transfer window opens in July, and are holding out for more than £50million for the former Celtic man.
It had been suggested City were front-runners for van Dijk's signature with one report over the weekend stating a deal worth £200,000 a week had already been agreed.
Such talk is premature, and it has now emerged Chelsea remain just as keen on van Dijk and, like Liverpool and City, view him as their top defensive target this summer while preparing their own lucrative offer.
However, the ECHO understands Liverpool are willing to compete with both their rivals by offering van Dijk a similar financial package.
Nevertheless, the Reds still believe money will not be the decisive factor and have been encouraged by the feedback received from van Dijk's representatives.
But City and Chelsea have both put forward their own strong cases with the decision now ultimately down to the player.
Liverpool, meanwhile, are still working to seal their first major signing of the summer as their pursuit of Roma winger Mohamed Salah reaches a conclusion.
The Reds have been in talks with their Italian counterparts over the 24-year-old Egypt international.
It's believed personal terms have been verbally agreed with Salah, who turned down a move to Anfield in 2014 when opting to join Chelsea instead.
Now the clubs are still discussing a fee with Liverpool having already seen a £28m offer rejected.
Source: Liverpool Echo
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