Liverpool have been hunting the Dutchman all summer to bolster their backline.
But ahead of tonight's 11pm deadline, the Reds have not made a bid for the centre-half.
Chelsea and Manchester City have also been linked with Van Dijk, but Anfield appears his most likely destination.
However, Southampton have remained adamant they will not sell, despite the 26-year-old's desire to go.
And according to the Daily Mail, the Saints are '99.9 per cent' certain they will keep Van Dijk.
Reports have suggested Liverpool are ready to pay Southampton £70m for the defender.
But it is unclear whether that fee would even be enough to persuade the Saints to sell.
The Daily Mail add they will have to receive a 'ridiculous' offer to even consider letting Van Dijk leave.
He arrived at Southampton's training ground this morning but remains isolated from the first-team squad.
It remains to be seen if Liverpool will firm up their interest with an official bid.
The Reds remain wary of making a move without being given encouragement, having been accused of an illegal approach earlier this summer.