The long-term Liverpool target plans to appeal a club fine for refusing to play in pre-season friendlies but Saints say their stance has not been changed by the 26-year-old's announcement.
Antonio Conte has also seen Nathan Ake leave the club to join Bournemouth in a 20 million pound deal.
Much will depend on whether the Saints relent and allow him to leave.
It meant he was unable to travel to England for PSG's 2-2 draw with Arsenal in November.
Van Dijk was born in Breda, Holland, on July 8 1991.
"Who wouldn't want to go to Barcelona?" United and Chelsea could both do with a player comfortable at both right-back and central defence.
Meanwhile The Guardian reports that the Reds are steadfast in their refusal to listen to overtures from Barcelona for Philippe Coutinho despite claims they "are prepared to pay £100m for the Brazil international".
It's hard to see Conte providing any comparable type of guarantee, and while it's certain he would welcome Chelsea signing Van Dijk, the centre-back might find it difficult to establish himself immediately as an automatic choice.
Their stance is set to be strenuously tested given there's only a few weeks remaining before the transfer window is shut with an offer between £50m-£70m, as The Times writes, enough to possibly change the club's mind. Me and my family have had the best time in my career here.
Pundit Tony Cascarino described van Dijk as "even better and quicker than Rio Ferdinand".
Carragher continued to explain his point by commenting on FC Barcelona's attempted move for Philippe Coutinho. Such irresponsibility has led to speculation that he may never play for England again.
As per The Sun, the Liverpool manager is ready to put faith in his current back-four and will not pursue his interest in the Southampton no.17. Dejan Lovren and Ragnar Klavan have struggled to maintain consistency, thus accentuating the need for a quality defender.
So what are you waiting for?