The 23-year-old forward, who has joined from PSV Eindhoven for an initial fee of £38million, is set to make his debut in the FA Cup tie at home to Wolves.
There are parallels with Van Dijk, as Gakpo's fellow Dutchman also made his first appearance for the club in a third-round tie having agreed a move prior to the January transfer window opening.
While manager Jurgen Klopp will give Gakpo plenty of time to acclimatise, the expectation realistically - considering his form this season and the impact Luis Diaz had arriving last January - will be for him to contribute significantly and provide the spark Liverpool need up front as Darwin Nunez continues to miss chances.
"I think he will handle it fine but you have no idea what it is like until you are under this sort of pressure," said Van Dijk, who is set to miss the next month after a hamstring injury at Brentford on Tuesday proved to be more serious than first thought.
"He will have to keep his head down and look at what we are doing as a group and listen to the manager, listen to the players around you and don't listen too much to the outside world because you can be one of the best in the world one day and one of the worst the next. It is never something in the middle.
"He has to stay calm and I think he will do that. He is that type of person."
Gakpo's 13 goals and 14 assists, plus his form at the World Cup where he scored in each of the Netherlands' three group matches, made him one of Europe's hottest properties and Liverpool swooped in to fend off interest from the likes of Manchester United.
He joins a misfiring forward line which now numbers six, although three - Roberto Firmino, Diaz and Diogo Jota - are injured and none are in any sort of form, with the club having just been humiliated at Brentford to leave them seven points off the top four.
"I think he can be very good for us. I feel like he will and he probably needs a bit of time," added Van Dijk.
"We need quality players and we need players who can decide games and I think over time he can definitely be one of those players, hopefully."
Van Dijk's injury adds him to the list which also includes midfielders James Milner and Arthur Melo.
Klopp said they will take a closer look at the data to see if something could have been avoided but believes the best solution is fewer matches - and better squads.
"We always try to figure out exactly why things happened and if we made a mistake we will not make it a second time, I can promise that at least," he said.
"But unfortunately, things happen and we have to deal with it.
"There are a few players who play for their club all the time and their national team all the time. I think in the Premier League Harry Kane would have exactly the same number of games. That is the highest level of intensity.
"If you ask me now whether it would have been a good idea to leave Virgil van Dijk out against Brentford then yes. Did anybody think about leaving him out? No. Him included. There was no reason for it.
"This is what I am talking about all the time when I say we have to reduce games, FA Cup replays or whatever.
"People tell us to leave them out and rotate but who leaves their best players out? It's not that easy.
"We have to sort that in the future with bigger squads and more level squads internally. Is that possible? I don't know. But it's probably the only way to deal with it for international and club teams.
"It's the direction we have to develop in if nobody reduces the games."