The Oranje have a selection dilemma as they consider a replacement for the injured midfielder while the Central Americans have slight concerns over their star keeper.
De Jong was forced off just nine minutes into his country's 2-1 last-16 win over Mexico and subsequent scans revealed a groin muscle tear, ruling him out of the remainder of the tournament.
PHOTOS: U.S. fan reactions | Beautiful people in Brazil
Consequently, Louis van Gaal has a tactical dilemma. He could switch to 4-3-3 or continue with the double pivot in front of the five-man defense with which he has started every game, replacing De Jong with Jonathan de Guzman, Jordy Clasie or versatile defender Daley Blind, who moved into midfield against Mexico.
If the latter option is taken, Bruno Martins Indi would be the obvious man to step in on the left side of the defense, as he did in Fortaleza. Regardless, Daryl Janmaat is expected to return on the opposite flank in place of Paul Verhaegh, who did not impress against Mexico.
As for Costa Rica, goalkeeper Navas, who has been one of the stars of the tournament, missed training on Wednesday because of a minor shoulder problem, but is expected to start.
Meanwhile, versatile defender Miller is doubtful because of a muscle tear in his left foot, which is a major concern given center half Oscar Duarte is suspended for the last-eight meeting with the Dutch.
Elsewhere, coach Jorge Luis Pinto is not expected to make any changes to the side that has served him so well in Brazil, meaning lone striker Joel Campbell will once again be supported by Bryan Ruiz and Christian Bolanos from out wide.