Barcelona's new striker and his representatives were in Lausanne on Friday morning for the six-hour hearing as they attempted to persuade the Court of Arbitration for Sport (CAS) to halve his suspension.
The CAS told Bryan Swanson, Chief News Reporter for Sky Sports, that a decision would be made "probably before the end of next week".
Swanson added that lawyers for the Uruguayan Federation said they expected a CAS decision "within the next ten days".
Suarez, 27, was also handed a nine-match international ban and £66,000 fine for biting Italy's Giorgio Chiellini during Uruguay's 1-0 World Cup victory on June 24.
Suarez’s lawyers left CAS headquarters at lunchtime having argued the incident took place while the former Liverpool star was playing for his country and should be limited to international football.
The Panel of CAS arbitrators consisted of the president, Mr Bernhard Welten from Switzerland, his compatriot Dr Marco Balmelli and Professor Luigi Fumagalli from Italy.
It has been reported that Suarez's legal team are confident of obtaining a reduction to two months and for their client to be allowed to train with Barcelona for the duration of his suspension. If successful, he would be available to return to action on August 25.
Suarez's lawyer and adviser Alejandro Balbi, also a member of the Uruguay FA's executive, admitted there was less chance of overturning the nine-match ban, but said there is scope for the four-month suspension to be reduced on the grounds that it infringes the player's fundamental rights.
Barcelona paid Liverpool £75million for Suarez after he received his FIFA ban, which, as it stands, keeps him out until October 25.
FIFPro, the world players' union, supports a reduction in Suarez's punishment at domestic and international level.
A statement on the organisation's website read: "That Luis Suarez has been trialled and vilified in public, ever since the incident, is a sanction in itself.
"On the other hand, it has been remarkable to see the response from his fellow professionals and the victim himself, Giorgio Chiellini.
"Many agree the sanctions are excessive. This is an important signal for the CAS panel to consider. The sanctions are a disproportionate response to the offence.
"Especially the four-month ban from all football-related activity, which is unfair for Suarez as it infringes his right to work at club level.
"In the international arena, where the offence was committed, a nine-match ban for Uruguay is also too strong as it effectively equates to a two-year sanction.
"FIFPro states the educative nature of the sanction mentioned by FIFA in the ruling can be much better achieved by making it partially conditional, including the obligation for Luis Suarez to receive treatment.
"This can be applied on the number of matches but also on the period of the ban. The FIFA appeals committee missed an opportunity to take this into account. FIFPro expects that CAS will respect these assumptions."
You can watch Barcelona, with or without Suarez, from August 12 live on Sky Sports 5HD - Your New Home of European Football.
Now he is at Barcelona the ban will most likely be reduced.- jfrench