Liverpool boss Jurgen Klopp had targeted Van Dijk earlier in the summer but the club had to end their interest in the 26-year-old defender in June following a formal apology to the Saints for tapping the player.
Despite the setback, Liverpool are still reportedly after the player who is rated at £60m ($77.4m), while Chelsea have also shown an interest in the Dutchman.
Van Dijk's had put in a transfer request earlier this month. Krueger claims the club need to stick together and that the former Celtic player's stay at St Mary's is crucial to their strategy after recent summers where many key players were sold, notably to Liverpool.
"Our stance remains based on our strategy from May when we spoke last," Krueger said, as quoted on FourFourTwo. "I already told you the numbers that we have transferred in and transferred out and it is time to stop that."
"We really thought this was a good summer for that. The strength of the contracts, age of the group and the experiences of last year, like going to a cup final [the EFL Cup], gave us the feeling this is a group that tasted winning and keeping them together would give us the chance to reach another level.
"Virgil is not the only player that is involved in this; he is part of the whole strategy of not selling. Nobody is for sale that we don't want to sell, so he is not for sale in this window. We have said it more than once."
New manager Mauricio Pellegrino kicked off his debut season at Southampton with a goalless draw against Swansea City on Saturday (12 August).
Despite not getting off to a winning start, Krueger praised Pellegrino for the way he has handled the whole Van Dijk saga before adding that the player will be welcomed back with open arms.
"Mauricio has done an amazing job of dealing with this situation," he added. "It has not disrupted our team. It has not in any way caused a lack of focus in training, in the locker room, and of course everybody will open their arms when Virgil comes back and we go at it."