Louis van Gaal's men face Argentina in Sao Paulo on Wednesday and the coach confirmed that captain Van Persie and defender Janmaat could be absent due to stomach problems.
Feyenoord defender Janmaat has not featured since the group stages of the competition, but Manchester United striker Van Persie missing out as Netherlands aim to reach back-to-back World Cup finals would come as a severe blow.
"Van Persie and Janmaat have not participated in training because of gastrointestinal complaints," Van Gaal told a press conference. "We do not want to take any chances."
On the prospect of Van Persie being at full fitness to face Argentina, Van Gaal added: "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."
There was better news for Van Gaal after Nigel de Jong took part in training on Tuesday.
The 29-year-old Milan midfielder injured a groin muscle during Netherlands' last-16 win over Mexico and the initial prognosis suggested he would be sidelined for two to four weeks.
"We had Nigel training today," said Van Gaal. "We now have to wait for the response."
Experienced defender Ron Vlaar and midfielder Leroy Fer also trained despite concerns over respective knee and thigh complaints.
Both could now play a part in a match that Van Gaal believes is too close to call.
"I think there is no favourite. It is a 50-50 match," he added.
