The availability of Atletico Madrid striker Costa (hamstring) has been a concern for the reigning world and European champions.
But, just a day after saying he was unsure about Costa, Spain coach Vicente del Bosque was optimistic about the 25-year-old's chances of featuring in Brazil.
Manchester City winger Navas (ankle) is also recovering well, with Spain set to face Bolivia in a friendly on Friday.
"It looks good for them (Costa and Navas)," Del Bosque told a news conference.
"Tomorrow (Friday) they will have a medical check-up, Costa will have some procedures done and it looks like Navas is doing well.
"We will evaluate their condition and make a decision on Saturday morning."
Barcelona midfielder Gerard Deulofeu, who spent the season on loan at Everton, was called up by Del Bosque for the Bolivia friendly.
Del Bosque said the 20-year-old deserved to be part of the squad for the friendly, and would be a handy back-up if needed for Brazil 2014.
"We've called up Deulofeu because of his merits. He's a player's man and he deserves to be in the squad, that's the first thing," he said.
"The second is that we want the young players to feel that they have a chance to get to the national team.
"We believe in him and if from June 2 there's a serious injury we'll have him ready because of his qualities. He's a player that has different qualities, there's very few players that have his qualities, and that's why we like him.
"We've done this before in the past with (Martin) Montoya and other youngsters and it's been a little tough sometimes because we don't want to interrupt the process that young players have to go through."
