The Atletico Madrid striker was substituted off in the ninth minute of the UEFA Champions League final against Real Madrid due to a hamstring injury, casting doubt over his fitness for Brazil.
But Costa is set to get some time in Spain's friendly against El Salvador in Washington DC on Saturday.
The front man said he was confident of breaking into Vicente Del Bosque's side.
"I think I feel pretty well. I was recovering for that week after the Champions League final and it's been a while since I've been fully able to recover," Costa said.
"Now I want to train because I've hardly done anything over the past several weeks, the only thing that matters now is training a bit. Will I be fit in time for the World Cup opener? Of course, why not?"
Costa said he had flirted with the thought of missing out on the Brazil spectacle, admitting his injury could have been even worse than it is.
"Of course the thought that I might miss the World Cup crossed my mind, I was afraid it was something more significant," he said.
"I thank the Mister (for calling me up) and I'm going to try and give my all to repay his confidence in me.
"I want to show him that I was worth all the trouble."
Costa said he is being held back by Spain's medics, as the World Cup grows nearer, with the defending champions' date with the Dutch on June 13.
"I want to train normally, but they won't let me," he said.
"I have to speak with the doctors, but I think I can play.
"I'm very happy. This is something special for me. I hope I can do as well as I did this season."
