Many fans had anticipated the Dutch defender would move on at the end of his contract.
While his present deal runs out in the summer, Van Dijk is eager to remain a Red and play for Arne Slot into the future.
While on international duty, Van Dijk said: "At both teams, I am still Virgil van Dijk, the big leader! And I certainly want to remain that for the next two years. I am human, I have emotions too.
"You start thinking all kinds of things. Especially just after a game like the elimination (by England) in the very last minute.
"I also understand that it came across unclear on how I stood in all this because after the match I was so disappointed and full of emotion. It perhaps came across as if it had been my last international match. I did have doubts that night and I did hint at that.
"It's very good that I went on holiday the next day, was able to spend time with my children, my family, which is the most important thing in my life. I was able to share it and then very quickly things calmed down."
