The club said on Friday it will do all it can to find the fans responsible for monkey taunts directed at Santos goalkeeper Aranha in Thursday's Brazilian Cup match in Porto Alegre.
Aranha complained after the slurs were chanted behind his goal near the end of Santos' 2-0 win at Arena Gremio.
Gremio said it will analyse television images and security camera images to try to identify the fans.
One young woman can be clearly seen yelling "monkey" from the stands, and local media said she was identified though social media networks and reportedly was suspended from her job because of the case's repercussion.
"If those responsible are identified as club members, they will be immediately suspended and prohibited from entering the stadium,"Gremio said in a statement.
"Everything we find will be turned over to the police so they can take the necessary actions."
The club said the taunts were "isolated acts by individuals" and "don't represent the grandiosity and the respect of the Gremio fans."
Aranha was expected to file a police report on Friday to formalise his complaint. He said fans also made monkey noises toward him.
The match was briefly interrupted as the goalkeeper talked to the referee, making monkey gestures and pointing to the fans.
The incident was included by the referee in the match report and Gremio is expected to face a suspension.
The team was fined about $US35,000 ($A37,900) earlier this year for fans' racist insults against another player at the Arena Gremio.
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