Last week, the Dutchman, who joined the Saints from Celtic in 2015, criticised the club for not allowing him to move on.
Liverpool were favourites to land the 26-year-old, but earlier in the summer, the Merseyside outfit were forced to withdraw their interest and publicly apologise after being accused of tapping up.
Even though Van Dijk has made his intentions clear, the Southampton hierarchy are not prepared to weaken their stance.
"Virgil is not for sale in this window and it's not personal," the Liverpool Echo quotes Krueger as saying. "It's not about him, it's about an overall much, much, much bigger picture - a change of course for Southampton.
"The first summer I was here five players went out and six went in, not counting academy. Second summer three went out, seven came in, and third summer five went out, five came in.
"Now it is one out and two in, and this is who we want to become. We want to mature, we want to be a team that can profit from synergies that create a much more attractive football and a better product for the fans, and gives us a chance to get back into Europe."