The Chelsea striker has started the campaign in superb form, scoring nine goals in seven Premier League appearances following his switch from Atletico Madrid.
Costa, though, has been consistently troubled with a hamstring problem, with club boss Jose Mourinho suggesting his training has been limited and he should not play three games in quick succession.
Having failed to score in five appearances since switching his allegiance to Spain from the country of his birth Brazil, Costa - who turned 26 on Tuesday - will be desperate to hit the target in Zilina.
However, Costa is not guaranteed to start after Valencia's Paco Alcacer scored on his first Spain start in their opening pool match with Macedonia last month, which finished 5-1 in Spain's favour.
Alcacer's club-mate Rodrigo is another forward option after he earned his first senior call-up, while Bayern Munich's versatile left-sided player Juan Bernat could also make his international bow.
"Right now I’m playing more as a full-back, but I’ve spent my whole life playing on the wing; I will play wherever I’m needed," he said.
One man who will not feature for the reigning European champions is Real Madrid defender Sergio Ramos - who withdrew with a calf injury on Monday - with Barcelona's Marc Bartra taking his place in the squad.
The inclusion of Bartra's club-mate Gerard Pique has caused some controversy, as questions were raised over his commitment to Spain after he backed calls for Catalonia to hold a vote on independence.
However, Barca forward Pedro insists Pique is fully behind Spain's cause, saying: "Pique is eager to help the team. With the national team he always plays at a high level."
But since Jan Kozak was appointed head coach in July 2013, Slovakia have lost just three times in 11 matches - winning five of their past six outings.
"We aren't going to stand there and stare at the Spanish players," he said.
"We want to compete with them and try to make things difficult for them."
