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.