Malaga general manager Vicente Casado sounded a note of cautious optimism after the club made their appeal against a ban from European football at the Court of Arbitration for Sport.
In December, UEFA banned Malaga from playing in Europe for two years, later reduced to one, for violations of financial fair play rules.
Malaga's appeal was heard in Lausanne on Tuesday, and CAS have said a verdict is likely next week.
In a statement on Malaga's website, Casado said: "It was a very difficult process, but we're pleased with how it went. I believe we put our case across well."
According to a statement on the CAS website, a verdict will be issued during the week commencing June 10.
Malaga finished sixth in La Liga this season, a place which would bring with it a Europa League qualifying berth.
With UEFA unable to plan fixtures until the case is resolved, several clubs are following it with interest.
Thanks to Atletico Madrid's success in the Copa del Rey, the clubs who finished fifth, sixth and seventh were eligible for the Europa League.
Rayo Vallecano, eighth, were in line to benefit from Malaga's ban but they have been denied a European license by the Spanish FA, which means the place could pass to ninth-placed Sevilla.
Rayo Vallecano have indicated they too could take their case to CAS.