The Uruguay international heads to the World Cup next week on the back of a match-winning double in the 3-1 victory over Southampton which took his tally for the club to seven in his last 10 appearances.
After a shaky start, which saw him miss three matches after a red card for headbutting Crystal Palace's Joachim Andersen in only his third game for the club, Nunez has rapidly become a fan favourite.
His arrival from Benfica, in what could turn out to be a club-record £85million transfer, placed a large burden on a player who only turned 23 in the summer but - despite starting afresh in a new country where he barely speaks the language - the South American is starting to flourish.
Van Dijk, who knows all about shouldering the weight of a hefty transfer fee after his 2018 £75m move from Southampton was a world record for a defender at the time, has seen the progress first hand.
"We never doubted his quality but obviously, when you have price tag like that and the goals are not flowing like you want, it's good (he has shown character) and I think he's done very well," said the Holland captain.
"Obviously he has all the qualities for a modern-day striker.
"There is a reason why we bought him and he's maturing, he's stayed patient, kept his head down and played and that's a credit to him and hopefully he can keeps scoring and stay important for the group.
"Obviously he learns how we want to play, he learns what we expect from him, he plays a little bit on the left but also has a free role coming into the middle.
"It takes time you know. It is a new team, new environment, new country, new language so it is absolutely normal for him to take a little bit more time (to settle in) but there is no doubt the qualities are there and the goals will follow."
While Nunez is an emerging talent, Liverpool's player of the season so far goalkeeper Alisson Becker has maintained a higher level while team-mates have been struggling for form and he was just as instrumental in the win.
The Brazil international made three crucial saves after the break from Mohamed Elyounoussi, Samuel Edozie and first-half goalscorer Che Adams to deny new Saints boss Nathan Jones hope of getting something out of his Premier League debut at Anfield.
"You shouldn't take anyone for granted. We certainly never do that," added Van Dijk.
"He's important for the group on and off the pitch. We don't want him to have to make saves, first and foremost. He had to do so (against Southampton) and he was outstanding.
"Brazil are a very good team, they have two of their best goalies in their squad and in my opinion the best goalie in the world is Alisson."
One Brazilian who will not be going to the World Cup is scorer of Liverpool's opener Roberto Firmino, whose ninth goal of the campaign is only two short of his tally for the whole of last season and equalled his return for the 2020-21 campaign.
"I think Bobby should be in, but who am I to say that?," said the Dutchman.
"He took it on the chin, all you can do is recover and be ready for the rest of the season and I think he will do that."
Southampton came to Anfield and were punished for being far too open in the first half and Jones accepts that is an area to work on.
"We have only kept one clean sheet as a club so that has to change," he said.
"We were really passive first half. We allowed world class players too much space and that is borderline suicide.
"That is something we address. We will work on the negatives and be better in the next game."