The Manchester United striker did not train with the squad on Tuesday due to a stomach problem, while Nigel de Jong did take part despite being ruled out of the tournament
The Manchester United striker has scored three goals during the Oranje's march to the semi-finals but could now miss the fixture against Alejandro Sabella's men after sitting out training on Tuesday.
“Van Persie had some intestinal problems so it was best he didn’t train," Van Gaal told reporters on Tuesday.
Asked whether Van Persie is 100 per cent ready to face Argentina, Van Gaal replied: “I don’t know. Tomorrow I will have to take these decisions. We have more than a day to go and Van Persie is a very important player to us.”
Should Van Persie fail to return to fitness, Klaas-Jan Huntelaar is likely to replace him. The Schalke striker scored the winning goal in the round-of-16 victory over Mexico.
Nigel de Jong also returned to training despite being ruled out of the tournament with a groin problem and Van Gaal admits the midfielder could potentially feature against Argentina.
"He tried out today and we will have to wait and see how it looks tomorrow," said the Netherlands coach.
"If you want to return to the pitch so quickly there has to be a reaction. We will see how he reacts. [Ron] Vlaar is the same. We'll see tomorrow."