Suarez was handed the suspension, and a nine-match international ban by football's governing body FIFA, after he bit Italy defender Giorgio Chiellini at the World Cup in Brazil in June.
Barca have since bought the Uruguay striker from Liverpool and the 27-year-old is due to return to action at the end of October.
He could make his debut in the 'Clasico' against Real Madrid on the weekend of Oct. 25-26 depending on the outcome of his appeal.
According to media reports, CAS has agreed to fast-track its verdict and it could be known by mid-August.
(Reporting by Iain Rogers, editing by Tony Jimenez)
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