Van Dijk's deal now has less than 12 months to run, with talks over an extension yet to open.
After victory over Brentford, the defender said: "I am very calm. The thing is, I want to play the best season I can. I want to be important and stay important for the club, Then we will see. Everything happens for a reason but for now, there have been no changes in my situation. I am very calm about it and there is no reason for me to start thinking for something else. I have a whole season left to play.
"I am proud and (Anfield) is home and it is a special place and what I said before, whatever happens in the future, Anfield is a special place in my heart. Let's see what the season brings.
"I am not playing football to lose or not become successful. It is not guaranteed but I want to win. We know how difficult that is. But playing for Liverpool, one of if not the best clubs in the world, there are expectations. I am really enjoying it so far and there is still so much to improve. Let's see what the season brings."