The Netherlands centre-half, who has kept three clean sheets so far this term, told The Guardian that it is important to back up such performances with silverware.
"This is a great time to be a Liverpool player," Van Dijk said. "Everyone is excited, everyone wants to be a part of it and though we know the season is very long, with four competitions to play in, we want to win everything. That is basically our mindset.
"You need to have ambitions, and with the size of this club and its history we are going to try to win everything. It is going to be hard, and there will be days when we have downs, but we have shown we can react to tough situations and at the moment I am not worried about anything.
"There is a lot of belief in this team, in the whole squad in fact. Everyone is there for each other."
Liverpool return to domestic action this weekend against Southampton.