Central defender van Dijk has been an impressive performer since joining Liverpool from Southampton in January, with his leadership and defensive qualities being seen as one of the major factors in the Reds' defensive improvement this season.
Indeed, the 27-year-old has been heralded as one of the best defenders in Europe, although he is not immune from making mistakes, as he gave away a late penalty during Liverpool's draw with Manchester City last weekend, a spot-kick that was ultimately missed by Riyad Mahrez.
Van Dijk was also at fault during the Netherlands' 2-1 defeat to France in the UEFA Nations League last month, as he was outjumped by Olivier Giroud for the winning goal.
Koeman was critical of van Dijk following that mistake and he believes there is still room for the former Celtic star to improve.
"I told Virgil within 30 seconds of the end of the game against France what I thought," Koeman told reporters. "I know him so well - and that means I know where all his little faults are.
"Virgil has to improve, not a lot, but sometimes he is a little too laid back. That needs to change."
Koeman should know van Dijk better than most, as he signed the defender for Southampton back in 2015, while he also named him captain of the Netherlands earlier this year.