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.
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If the latter option is taken, Bruno Martins Indi would be the obvious man to step in on the left-hand side of the defence, 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 centre-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.