Having finished third at the World Cup under Louis van Gaal, Netherlands have struggled to find form in the Euro 2016 qualifiers.
An opening-match defeat against the Czech Republic came after a 2-0 friendly defeat to Italy in early September.
Things looked to be getting worse for the new Dutch boss when Kazakhstan led 1-0 after an hour in Amsterdam in their second group match, but Klaas-Jan Huntelaar, Ibrahim Afellay and Robin van Persie secured a 3-1 win.
They failed to build on that, though, as a Gylfi Sigurdsson double gave Iceland a 2-0 on Monday, leaving Netherlands six points adrift of the Group A leaders in third.
Hiddink's shaky start to his second spell at the helm has led reports the 67-year-old could leave his position, but De Boer is adamant he would not be interested in replacing him were that to happen.
"Like any fan I did not like that the Netherlands crashed against Iceland," De Boer told AD. "The only remedy is to grab points.
"Whether I'm available if necessary? No, certainly not."
Earlier in the week Southampton manager Koeman was the first to rule out replacing Hiddink, insisting the Dutch football association missed their chance when he left Feyenoord in June.
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