Van Dijk has earned rave reviews for his performances for Neil Lennon's team since his £2.6m transfer from FC Groningen.
The centre-back has been capped for his country at U19 and U21 level, and Van Gaal confirmed he was watching the 22-year-old ahead of Celtic's recent Champions League double header with Ajax.
AC Milan midfielder Nigel de Jong spoke enthusiastically about his compatriot after their visit to Celtic Park last week in the same competition.
Asked about De Jong's comments, the Celtic star 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.
"But all I can do is to continue playing well and win the games with my team."
Van Dijk is awaiting his first full international cap and he is aiming to take his chance with World Cup places up for grabs.
He added: "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."