"There's a lot of pressure from England and Italy," Balbi told local Uruguayan radio. "We're polishing off a defence argument."
FIFA is investigating the incident during Tuesday's Group D match in Natal which has made headlines around the world. Uruguay's win took them through to the last 16 where they will face Colombia on Saturday.
Balbi and FA boss Wilmar Valdez were travelling to Rio de Janeiro on Wednesday morning to present their case. Valdez told local radio that Suarez would not be speaking at the meeting.
Suarez, twice previously banned for biting, could be hit with another lengthy suspension despite escaping punishment during the match for the incident involving Italy defender Giorgio Chiellini.
"There is a possibility that they ban him, because there are precedents, but we're convinced that it was an absolutely casual play, because if Chiellini can show a scratch on one shoulder, Suarez can show a bruised and almost shut eye," Balbi said.
"If every player starts showing the injuries he suffers and they open inquiries for them everything will be way too complicated in the future. We're going to use all the arguments possible so that Luis gets out in the best possible way."
His argument echoes the sentiment in much of Uruguay, which is jubilant at the team's last-gasp victory and largely backs their key player.
The Liverpool forward's lethal finishing is far more important than his straying teeth, say many in the small, sleepy agricultural country vying for a third World Cup triumph.
Local media gushed about the victory over Italy and put the "supposed" bite on the backburner, accusing other countries of launching a 'manhunt' against striker.
"'Monster': The British press' new manhunt against Suarez," said leading newspaper El Observador on Wednesday. "English newspapers return to attacking the Uruguayan after the alleged biting of (Giorgio) Chiellini," the article read.
An article on the specialised Tenfield web page argued: "Brits fretting about Suarez should first explain how they won the 1966 World Cup with a ball that wasn't a goal."
Leading newspaper El Pais published an extensive article detailing defender Chiellini's "bad behaviour" in Italian clubs, complete with videos showing alleged foul play.
Many reporters are cautioning that it is unclear whether Suarez deliberately bit Chiellini, and argue that he may have been provoked into doing so.
Abroad, however, Suarez's behaviour has sparked outrage and calls for a tournament-long ban.
Balbi suggested that may be part of a broader conspiracy to sideline Uruguay, who lost to unfancied Costa Rica in their opening match without Suarez as he battled to complete his recovery from knee surgery.
"You shouldn't forget that we're rivals of many and we can be for the organiser (hosts Brazil) in the future. This does not go against what might have happened, but there's no doubt that Suarez is a rock in the shoe for many," Balbi added.
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