Van Dijk was one of six Saints players to pay for the 4-1 thrashing at the hands of Leicester City.
Van Dijk was on Liverpool's radar during the summer, but a bid from the Anfield side was knocked back and the Dutch global ended up staying at St Mary's.
A Marcos Alonso free-kick was enough to clinch victory for the Blues, but it was the man who spent the entire match on the substitutes' bench that caused most intrigue.
That Liverpool are looking for a new centre-back isn't exactly news, and that Virgil Van Dijk is their favourite for the job no longer surprises anyone.
Van Dijk had to settle for a place on the bench as Saints started with three in central defence
Martinez is Guardiola's other target in the new year, but "Van Dijk is the preferred option", with an enquiry likely "in the coming weeks".
"In that department we have too few players and to handle all competitions we are in trouble, real trouble if this is the case".
Southampton manager Pellegrino welcomed Van Dijk back to first-team action after he trained separately from the group for a period after putting in his transfer request. "And we miss an important player like Benjamin Mendy". "It always depends how they are, the energy they've got in every training session. I can have my opinion and this I have give to the technical director, to the chairman, my opinion", he told reporters.
"I will repeat that I can't control the market right now. The club was clear in the beginning and I have the same opinion".
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