Van Dijk is wanted by the Reds but their pursuit landed them in hot water earlier this summer.
Liverpool were forced into an embarrassing public apology after Saints accused them of tapping up the player.
The trail has since gone cold, with Southampton insisting the Dutch defender is going nowhere despite Chelsea joining the Kop club in the race to get him.
But the Liverpool Echo say Liverpool are ready and waiting for any change of plan from the south coast club.
Wesley Hoedt is set to join the club this week from Lazio in a £17m deal.
And with the centre-back a potential replacement for Van Dijk, Liverpool could yet launch a late bid to get their target.
If the Reds don’t land the Dutch defender, they won’t be signing anyone else.
It’s claimed Jurgen Klopp is happy to press on with his current four centre-back options of Joel Matip, Dejan Lovren, Ragnar Klavan and Joe Gomez.
Mamadou Sakho is still on the books, but won’t be joining the club.
