Suarez, the Uruguay Federation and his new club Barcelona, filed requests that the case be fast-tracked - almost exactly a month after FIFA banned the 27-year-old striker for nine competitive international matches and from any football-related activities for four months.
The Court released a statement that confirmed "it is likely that a final award will be rendered well before the end of August".
The world of football was left stunned this summer as Suarez bit an opponent on a football pitch for the third time - clashing with Italy defender Giorgio Chiellini during Uruguay's 1-0 World Cup Group D victory in Natal in an incident the referee failed to spot in 'real' time.
The FIFA Disciplinary Committee swiftly imposed a lengthy suspension and rejected a quick-fire appeal made by the Uruguayan football authorities, and Suarez's eventful summer continued when Barcelona paid Liverpool a fee in the region of £75million for his services despite the saga.
Although FIFA must agree to fast-track the appeal case, no hearing dates have been set and no arbitrators have yet been appointed to hear the case.
The news gives Suarez hope that a ruling will be made before the Spanish season kicks off on the weekend of August 23-24.