The Reds have been chasing the Holland international all summer long but the Saints have yet to receive a formal bid.
The Irish Independent say Southampton are relaxed about Van Dijk’s position as he continues to train away from the rest of his team-mates.
After Liverpool were accused of tapping up the 26-year-old earlier this summer, Saints are aware they hold all the cards when it comes to any transfer.
A fee of £70m could tempt Southampton into selling but the Reds have made no bid, according to the reports.
Former Arsenal star Nigel Winterburn thinks Liverpool will look very strong if they end up signing Van Dijk.
“They’re trying to (sign players), aren’t they,” he told Sky Sports.
“I think Van Dijk has been linked.
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“I looked at Liverpool at the weekend, every compartment was sensational.
“I think what you have to look at and say goalkeeper is still a question.
“Mignolet was in, left him out, needed a rest before an international break, Karius came in.
“Centre-half position. If Liverpool can bring in Van Dijk into that centre-half position, I think they would be looking very, very strong.”
Liverpool have had a busy couple of days, completing the signing of Naby Keita and making several offers for Monaco forward Thomas Lemar.
The Reds have already completed deals for Dominic Solanke, Mohamed Salah and Andy Robertson so far this summer.
