The Brazilian-born Spanish international is set to seal a move to Stamford Bridge, after Chelsea agreed to meet his buy-out of over £30million.
Costa is understood to have already passed his medical, and Sky Sports understands that a deal could be concluded by Tuesday - before the World Cup finals kick off.
Costa has now admitted that he is heading for West London, and spoke after Spain's 2-0 friendly win over El Salvador.
Asked if he was heading to Chelsea, he told Cadena Cope: "Well, it looks like that."
Costa has overcome injury concerns to make the World Cup squad and insists he is fully fit.
"The injury was there and there was a doubt, but I am in good shape now," he said.
Costa is heading to his homeland, having switched international allegiance to Spain, having played in two friendlies for Brazil - and he admits he is unsure of what the reaction will be.
"It will all depend on how people have interpreted things, but I am very happy and I will see when we get there what the reception will be," he added. "But either way I am happy to be at a World Cup with Spain."