CAS said Friday that Suarez, the Uruguay football federation and Barcelona have filed a request for a fast-track appeal against FIFA's ban for nine competitive international matches and four months from all football.
"It is likely that a final award will be rendered well before the end of August," the court said in a statement to The Associated Press.
The Spanish league season begins the weekend of Aug. 23-24, when Barcelona hosts Elche.
FIFA must also agree to a fast-track procedure.
No hearing dates have yet been agreed to, the court said.
Arbitrators have also yet to be appointed to judge the case. In typical appeals to CAS, both sides and the court each choose one lawyer on the three-member panel.
FIFA's sanctions imposed on Suarez also included a fine of 100,000 Swiss francs ($112,000) for biting the shoulder of Italy defender Giorgio Chiellini in a group match at the World Cup.
Uruguay beat Italy 1-0 with a goal scored one minute after Suarez's bite was missed by the match officials. The South Americans advanced to the second round, but without its star striker were easily beaten by Colombia.
FIFA's disciplinary panel imposed the ban on June 26.
In his submission to that hearing, Suarez wrote that he did not deliberately bite Chiellini, but had lost balance and fell with his mouth open on the Italian's shoulder.
Suarez later apologized, and Chiellini accepted.
The ban currently expires on Oct. 25, the same weekend that Barcelona is due to visit Real Madrid in the first "clasico" of the season.
Because Suarez is barred from all "football-related activity," he cannot train with his new club, which he joined from Liverpool this month.
If Suarez loses his appeal, he will also miss three Champions League group matches.
Uruguay's next competitive match is at the Copa America, which kicks off in June 2015 in Chile.