The Costa Rica defender has been sidelined for the past eight months after breaking his leg against Stevenage in the FA Cup.
While Oviedo is back in contention for the Toffees ahead of tomorrow night's third-round clash, Arouna Kone could also be involved following a year-long absence through injury.
"We have really good news with Bryan Oviedo being in the squad for the first time since his broken leg," Martinez is quoted as saying by Sky Sports News. "Arouna Kone could make his return as well. He is available for selection, but we need to be a little bit cautious.
"Brian is in a situation where he has been training with the group now for a while and I do think he is ready for 11-a-side after he played the game with the Under-21s."
Everton head into tomorrow's match on the back of a shock 3-2 defeat at home to Crystal Palace in the Premier League.