The 25-year-old Atletico Madrid striker has expressed his desire to represent Spain but the matter now looks set to be resolved in the courts.
The 25-year-old Brazil-born striker has already represented the Selecao at international level, but both of the games he appeared in were friendlies.
Consequently, after receiving Spanish citizenship in July, Costa is now eligible to represent la Roja, which, it was revealed on Wednesday, the attacker fully intends to do.
Brazil has responded to the news by canceling the player's call-up for the upcoming friendlies against Honduras and Chile, but Marin is pushing to stop Costa from representing the country he wishes to.
"From now on we'll deal about this with our legal department," he told reporters. "But Brazil will fight to the end to have the player playing for Brazil. We've been in direct contact with the president of the Spanish Football Association (RFEF), we told them our wishes, our disposition.
"We have a very good relationship with the RFEF. We'll fight to the last instance. The final word, of course, will be the player's. It seems to me that he has already decided, but that doesn't end the story. Within what is right in the sporting regulations, Brazil will go all the way and fight."
However, Brazil technical director Carlos Alberto Parreira feels that it would be a mistake to go against the wishes of the player.
"I'm not against the CBF's position - I was totally favorable to the CBF," he said. "But if he says he wants to play for the Spanish team, I think we need to consider this case closed. We'll be going against what the player wants otherwise."
Costa has been in sensational goalscoring for los Rojiblancos this season, netting 13 goals in 13 games in all competitions.