Oviedo fractured his tibia and fibula in an FA Cup tie against Stevenage in January, apparently ruling him out of the tournament in Brazil but Martinez said his recovery was ahead of schedule.
"Bryan is well ahead in his recovery time," Martinez told a news conference. "We have sent him back to Costa Rica because we are working with the national team who want to assess him."
"He saw an independent specialist in London before he went away and the specialist feels he can make the World Cup. That would be an incredible statement given he suffered the injury six weeks ago at Stevenage."
Oviedo, who had a rod inserted through his tibia, would be a key man for Costa Rica who are in the same group as England, Italy and Uruguay.
Costa Rica's first match is against Uruguay on June 14.
"It would be phenomenal for him personally if he was to make it," Martinez said.
"He has been very positive from the beginning. After two weeks he was on the bike. He's a quick healer but he's also got that positive mentality and he's got that goal of getting to the World Cup. He is a great example for anyone."
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