Klopp made the shock announcement on Friday that he will leave the Reds at the end of the season after nine years at the helm.
And now, to make matters worse for Liverpool fans, skipper Van Dijk has suggested, too, following Klopp out of Anfield.
The 32-year-old, who turns 33 in July, has revealed he is "very curious" about how the Reds replace their legendary boss.
Van Dijk, along with everybody connected to the club, remain in shock over the news, which is hard to process.
Given Klopp's announcement, such news has raised concern over the futures of the Dutchman along with teammates Mohamed Salah, who continues to be linked with a move to the Saudi Pro League.
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Van Dijk has 18 months remaining on his current contract and was asked whether the club's decision on Klopp's replacement will have an impact on his own future.
"The club will have a big job on their hands, that is well known," he said.
"To replace not only the manager but the whole staff and there are so many things that will change.
"I'm very curious which direction that will go in but when that will be announced we will see our situation.
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"It will be the end of Jurgen Klopp's era - I am still part of it that's why I don't like to talk about it - and that is my main focus.
"Hopefully we will have the success we all dream of and by then probably there will be more clarification about what the club wants for the future and then we will see."
Asked whether he could form part of the post-Klopp era, the Netherlands international replied: "That's a big question. I don't know."
Liverpool defeated Norwich 5-2 in the FA Cup fourth round on Sunday afternoon.
Attentions now turn to Chelsea in the Premier League who travel to Anfield for Wednesday's encounter, before Klopp's side take on Arsenal next weekend at the Emirates.
"Nothing has really changed," Van Dijk added.
"Obviously things will change at the end of the season and in the new season but at the moment it doesn't and we have to keep doing the same things.
"It's easier said than done but I sense the rest of the boys think like that as well and it is the job for me to ensure we keep it that way.
"We are all human beings and we have emotions - some players feel different about the manager's announcement than others.
"That's absolutely normal because everyone thinks in different ways but I didn't notice the professionalism being dropped or the level of standard. The training sessions I have seen in the last couple of days were not different than before.
"For the boss it (the Norwich game) was a bit different but for us it was to make sure we got to the next round with some players coming back from injury and now we focus on Wednesday.
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"We can speak about the situation, about what will happen next year, every week but it doesn't change, it's noise we don't need and that's why we focus on getting the job done and that's why I feel nothing has changed.
"It is still the same but at the end of the season there will be different things happening of course, but that is for the club to sort out."