The 25-year-old striker opted to represent Spain, where he plays his club football for Atletico Madrid, and made his debut for them in a friendly against Italy in March.
Scolari claimed that he had spoken to Costa about playing for Brazil prior to his decision to choose Spain.
However, Costa said that such an approach never happened.
"Scolari never called me by telephone," said Costa. "The only coach that I spoke with was (Spain's Vicente) Del Bosque who showed interest in me, invited me for a meal and made me realise that I was in his plans.
"I am Brazilian and that is not going to change but I want to win the World Cup with Spain."
Costa was responding to comments on Friday by Scolari who told O Estado de Sao Paulo: "I was going to call him up for the World Cup. Was I wrong? I don't know.
"He would be at the World Cup with Brazil. I spoke to him two times about it.
"The problem is that there are other interests behind everything. With Diego Costa a Spanish citizen it opens doors in Europe."
Costa heads into the World Cup off the back of a superb season for Atletico Madrid.
He scored 36 goals as the side won the Spanish title and reached the Champions League final.
Costa first moved to Atletico in 2007 and spent time on loan at former club Braga, Celta and Albacete before moving to Vallodolid in 2009. He returned to Atletico in 2010.