Oviedo is recovering from a serious leg break injury suffered in January.
"Bryan is well ahead in his recovery time," said Everton's manager. "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 this week 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 only six weeks ago at Stevenage.
"The World Cup is an incredible opportunity for him so that is why we are working together with the national team to try and get him fully fit. He will be in Costa Rica for the next two weeks and then will come back here.
"We are going to send some of our medical department over to Costa Rica with him because we want to do everything we can for him."
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