Following a 2-0 home triumph against Porto in the Champions League quarter-final first leg on Tuesday, four more matches separate the Reds from a sixth European crown.
With five league games remaining, Jurgen Klopp's team sit top of the Premier League with a two-point lead, although title rivals Manchester City have a game in hand.
No team has lifted Premier League and Champions League trophies in the same season since Alex Ferguson led Manchester United to domestic and continental glory in 2007-08.
The pressure mounts further when Liverpool's 29-year drought since their most recent league title is factored in, but van Dijk is not burdened by the weight of history.
Speaking to reporters at Anfield on Tuesday, Van Dijk said: "It's still something we need to believe and do, but if you think about it, what is nine games?
"You have to believe otherwise you can just stay home next time. Go for it.
"We played a tough team, good result, but it's not over. It'll be even harder over there [in Porto], but hopefully we do the job and go to the next round.
"We should be confident anyway, it's a great time to be a Liverpool player and, hopefully, there are nine games left if everything goes well, fingers crossed.
"We'll give everything we've got then have a well-deserved break after."
Despite the Dutchman's confidence in his team, Van Dijk refused to label Liverpool as the favourites to be crowned champions of Europe, even if their target is to reach the final for a second successive season.
"All the teams still in it have all the chance to win the trophy," the 27-year-old added.
"But we'll believe in ourselves to keep going and hopefully reach the final again, because that's what we're aiming for."
The Reds are in the middle of arguably their toughest run of matches, with Chelsea on tap Sunday before the return leg against Porto next Wednesday.