The goalkeeper put in a stunning display during extra-time and penalties as his side, down to 10 men, remarkably beat Greece in the last 16.
Navas' efforts, which came after Greece had forced an extra 30 minutes by grabbing a seemingly crucial equaliser in injury time, took Costa Rica to the last eight of football's biggest tournament for the first time.
The Central American side will, therefore, be desperate to have him available for the next phase - but they are waiting on the fitness of the 27-year-old after he sat out training with a shoulder problem.
"We have to be careful and keep an eye on that," team doctor Erick Sanchez told reporters.
"We chose to be careful with him and let him rest so he can play on Saturday."
Midfielder Celso Borges is among those hoping Navas is fit having waxed lyrical about the shot-stopper earlier this week.
“He was born on Mars or Venus or something," said Borges. "He’s fantastic. He has given us so much.
"He’s a leader on and off of the pitch. With his saves we always get second chances and he’s a great person. He deserves all this attention.
"The secret was already out I think, but this has taken him to centre stage. But we knew it from the start. I've known him for a long time. He’s awesome."
