The Saints will host Liverpool at St Mary's on Sunday a little over a month after Van Dijk made the switch to Anfield for £75m - a world-record fee for a defender.
Van Dijk is the latest in a long line of players to have joined Liverpool from Southampton in recent years, but the centre-back's saga was more controversial than most of those after he initially failure to engineer a move away in the summer.
"It will probably not be the most friendly. I am not sure. They were always really nice with [Nathaniel] Clyne, Adam Lallana they obviously missed most. Sadio Mane they were okay, I'm not 100% sure," Klopp told reporters.
"Virgil is the last one. We don't think about it. It will be more normal in the future but for now we have to go there and play football, and nothing else. I don't think anybody in Southampton would say we have stolen him. It was a very public deal.
"Yes, for sure, I will talk to Virgil about it. With other players I didn't talk about it because I didn't know or look where they were coming from. We are all human beings, we are influenced by circumstances. It will not be a normal game, how can it be?
"I think how football fans are, they want to disturb everything we try to do to help their team and they will whistle. Is it nice? I don't think so. Will it have influence? I don't think so but we will see but we cannot make it too big. We have to accept it how it is: loud, not nice maybe, but still we have to play football."
Liverpool have only won one of their last six meetings with Southampton across all competitions.