The Dutch centre-back has less than a year remaining on his contract with no signs of an immediate agreement on a new deal.
Van Dijk has been fundamental to Liverpool's success since joining for a then world record £75 million fee for a defender in January 2018.
A 2-0 win over Brentford on Sunday was his 100th Liverpool appearance at Anfield during which time he has suffered only two defeats.
"I'm very calm," Van Dijk told Sky Sports.
"I want to be important and stay important for the club. What happens? Let's see, but I'm very calm about my situation. There's no reason for me to think about something else because I have the whole season to play."
Van Dijk has won the Champions League, Premier League, Club World Cup, UEFA Super Cup, FA Cup and two League Cups during his time at Liverpool.
He is expected to be vital to helping his compatriot Slot instill his ideas as he faces the daunting task of succeeding Jurgen Klopp.
"Whatever happens now, Anfield has a special place in my heart. And it's been successful. Let's see what happens," added Van Dijk.
"Playing for Liverpool, one of the most if not the most successful club in the world. It feels great to wear the shirt.
"But there's so much for the club to improve on, for myself and the team, let's see what (the season) it brings."
