The QPR goalkeeper has been linked with a move away from Loftus Road since the club's relegation last season, with Harry Redknapp preferring to utilise Robert Green in goal.
With Cesar retaining hope of a place in Luiz Felipe Scolari's FIFA World Cup squad, a return to his homeland had been mooted, but Gremio chief Costa insists his club are not interested.
"There is no chance that Gremio will sign Julio Cesar. Our first-team goalkeeper is Marcelo Grohe," he told Radio Gaucha.
Costa's denial comes shortly after Cesar stated that talks were ongoing between his representatives and Gremio, adding he was grateful for their interest.
"The negotiations are very advanced and are well underway, but I have not signed anything yet," he told Globo Esporte.
"I am happy with Gremio's interest. It is a great club and playing in the Copa Libertadores makes it even more interesting to finalise the negotiation.
"I was given interesting information about the city of Porto Alegre. It is a great city to live in and I am thankful for their interest."
