The Reds top the early Premier League table ahead of champions Manchester City with four straight wins and maximum points.
Van Dijk, 28, said: “We want to keep going – and we want to win every game that is ahead of us now.
“There are seven games before the next international break. We want to win any match, and so seven wins is the target. That's what we have to try and do.
“It is very hard to say whether the same points total as last season would be enough this time. If you win your games, that is the only way to think.
“We know exactly how good Manchester City will be in the Premier League again this season.
“But there also the other competitions where we can look to have success. The next few weeks we will be playing Saturday/Tuesday almost all the time.
“So we know how tough it is going to be, both this next period and the rest of the season. But we have the mentality and the players to win every game ahead of us."