The Reds extended their advantage at the top of the Premier League courtesy of their last-gasp victory over Leicester on Saturday, combined with Manchester City’s shock home defeat against Wolves 24 hours later.
Jurgen Klopp’s side have yet to drop a point this season and have now won their last 17 Premier League matches stretching back to the start of March.
They can equal Manchester City’s record of 18 consecutive wins with victory against Manchester United at Old Trafford when the Premier League resumes after the international break on October 20.
That fine run of form has understandably raised excitement amongst the supporters, who are now dreaming of a first league title since 1990.
Van Dijk, though, is refusing to get carried away and says there is plenty of work still to do if they are to end that long wait for a title.
"So far we have been getting the points," he told Sky Sports.
"There is always room for improvement in our game. And I think we should just focus on all the games ahead of us and don't look at any gaps or points or difference between us and the others, including City.
"There are a lot of busy periods coming up as well with December and January and anything can happen still."
Van Dijk admits he was surprised by Manchester City’s home loss to Wolves, just their fourth home defeat in the Premier League under Guardiola in 61 matches.
"I think everyone expected a difficult game for City, but when City are at home it never really happens that they don't score at least one goal.
"It was a great performance from Wolves, and you have to give credit to them. But they (City) will try and bounce back from it. Until then I've just got to focus on international football.”