With eight consecutive wins, the Reds have an eight-point lead over reigning champions Manchester City.
"I did not expect it," Van Dijk told NOS of the successful start of Liverpool's season.
"I also did not expect that we would win eight games in a row, but the reality is that it is.
"It is better than standing here in a different situation of course. We are of course very happy at Liverpool."
He added: "You hear from many people that give priority to the Premier League over the Champions League and other competitions we participate in. However, we want to get as far as possible in every competition."