The former FC Groningen centre-back arrived from the Eredivisie in the summer as part of a £2.6million deal and has grown in stature as the unbeaten Hoops eased their way to the top of the Scottish Premiership.
And his performances in the Champions League against Dutch champions Ajax have been encouraging for Oranje boss Van Gaal as he starts the job of choosing his 23-man squad for next summer's World Cup in Brazil.
Van Dijk's hopes were also boosted when AC Milan midfielder Nigel de Jong claimed the 22-year-old was ready for international football despite his mistake in the 3-0 defeat to the Rossoneri last week, which confirmed Celtic's European exit.
Neil Lennon's side responded to that disappointment by putting seven past Hearts in Sunday's William Hill Scottish Cup clash.
But Van Dijk is not concerned that Van Gaal will see that Tynecastle thrashing as proof the Scottish game lacks the edge required to ready him for a major finals.
Asked about De Jong's comments, he said: "That was nice to hear from a very good player but, for that to happen, it's up to me to show everyone that I'm good enough and to play good games.
"Will results like Sunday's hinder my chances? I don't know. It's difficult for me to say how the national team coaches judge players.
"But all I can do is to continue playing well and win the games with my team.
"But I do think the Premiership is a competitive league - definitely. If you compare it to the Dutch league, it is quite similar. There only a few differences, like the physicality."
The Dutch will discover on Friday their three World Cup group opponents and Van Dijk would love to book his place on the flight to Brazil.
He said: "The World Cup draw is on Friday and I'm hoping that my country gets a kind draw. I'm looking forward to it - it would be great to be there."
Van Dijk was at fault for Milan's first goal at Parkhead when he failed to keep tabs on Kaka as the Brazilian superstar nodded in the first goal.
He also passed up a gilt-edged chance after the break that should have levelled the scores at 1-1.
But the defender says Sunday's crushing win over Gary Locke's men did ease the pain of his Champions League calamity.
"We all wanted a reaction after the Milan game," he said. "We knew it could be a difficult game away at Hearts, but we played very well and won the game. It was not difficult.
"The day after the Milan defeat was when the disappointment was at its worst, but after that we moved on to focus on the Hearts game.
"I was disappointed personally in the way we lost the goals last week, especially after watching the game back. But the day after that, you can't keep thinking about it. You have to move on and that's what I did."