The Court of Arbitration for Sport says the decision is "likely to be rendered some days" after the closed-door hearing in Lausanne on Friday.
The fast-track timetable was agreed on with FIFA, which also banned the Uruguay forward for nine competitive international matches.
Suarez's new club, Barcelona, has joined him and Uruguay's football federation in the appeal. (Suarez's apology)
Barcelona starts the Spanish league season on Aug. 24 at home against Elche.
If the court dismisses the appeal, Suarez's ban will expire Oct. 25.
FIFA suspended Suarez for biting the shoulder of Italy defender Giorgio Chiellini in a World Cup group match in Brazil.