The defender recently submitted a transfer request and criticised the club for refusing to sell him.
However, according to Yahoo Sports, the coastal club would consider a deal if Chelsea or Man City offered in excess of £70m for the Dutchman, who was widely reported to be keen on joining Liverpool.
The report adds that if the 26-year-old had agreed to be part of the pre-season squad after expressing a desire to leave, then Southampton may have sanctioned a move to Liverpool.
The Merseyside outfit were forced to issue an apology and withdraw their interest in Van Dijk after they were accused of tapping up.
It is believed that Southampton are hopeful of keeping their key man for at least one more year.