Although the 24-year old has already featured twice for Brazil, due to the fact that both games were friendlies he would still be eligible to play for Spain should they call him up.
Costa has netted seven times in his opening eight La Liga games so far this season, including the only goal in his side's Madrid derby victory.
Spanish newspaper AS reported that the World and European champions are keen on his services, but Costa says that he will choose to play for whoever makes the first move for him.
"Nobody has contacted me but I won't say no to whoever calls me up first. How would I say no to a national team manager?" he told Spanish television channel, La Sexta.
"Spain have strikers like Negredo, Soldado and Villa. They have the best ones, it's very hard to get called up."