Lawyers for the Barcelona striker travelled to the CAS headquarters in Lausanne, Switzerland to state their case, with the legal team were hopeful of CAS halving the ban to two months, meaning the former Liverpool striker would be available to play from August 25. They also want him to be allowed to train with Barcelona while he is suspended.
They were expected to argue that as the biting incident took place while playing for Uruguay in the World Cup then the ban should be limited to international football. Following the hearing, CAS issued a statement which read: "At the end of the hearing, the panel informed the parties that it will issue its decision as soon as possible, probably before the end of next week.
"The full arbitral award, with the grounds, will follow at a later date and be published by the CAS."
FIFA imposed a four-month ban from all football-related activity, plus a nine-match international ban and a £66,000 fine after Suarez bit Italy's Giorgio Chiellini during Uruguay's 1-0 win on June 24. FIFA's appeal committee later upheld the sanctions.
Barcelona paid Liverpool £75m for Suarez after he received his FIFA ban, which runs until October 25.