The 25-year-old has caused controversy by opting to play for Spain rather than the country of his birth
The 25-year-old Atletico Madrid star has caused huge controversy by opting to play for la Roja, despite representing the country of his birth, Brazil, in two friendlies earlier this year.
Now the CBF's juridic director Carlos Eugenio Lopes wants to see action taken against Costa.
"It's obvious that the reason he made that choice was financial," Lopes told O Globo.
"The chairman [Jose Maria Marin] authorised me to open a legal action at the Justice Ministry requesting that he loses his Brazilian citizenship, which Diego Costa has rejected.
"I have no doubt that he was allured. He suffered two hours of peer pressure from the Spanish on Monday night and another two hours on Tuesday morning.
"Diego Costa talks about love on the letter he sent CBF, but he chose Spain in the same year he played two friendly matches for Brazil and now on the same week he has been called up for two other friendlies.
"CBF was willing to fight for the player. Legally, our arguments are pretty strong because the friendlies are good enough for the Fifa ranking.
"Switzerland's 1-0 win over Brazil was what helped them go up to seventh and guaranteed them as head of selection for the World Cup draw. If they didn't consider the friendlies, would Switzerland have been seventh? No, that spot would've gone to Italy.
"The chairman told me that Costa has proved he's not fit to be part of the Scolari family, that he would contaminate the family because he's not committed to Brazil, but to Spain.
"He rejected his Brazilian citizenship. Marin has asked me to study the situation deeply in order to keep him from ever playing for Spain.
"He told me that, from now on, Costa is 'persona non grata' at the national team and that the players themselves wouldn't welcome him because of that episode."
Should Costa be allowed to represent Spain, it could potentially see him face Brazil at next summer's World Cup in his homeland.