Chief U.S. District Judge Claudia Wilken is expected to take the motion for class certification under consideration after hearing arguments at 2 p.m. and to issue a written ruling at a later date.
The case concerns several consolidated antitrust lawsuits filed beginning in 2009 by athletes including former University of California at Los Angeles basketball star Ed O'Bannon.
The lawsuits also name the College Licensing Co. and video game maker Electronic Arts Inc. as defendants.
The athletes claim the defendants have conspired to prevent them from being compensated for the use of their likenesses during TV broadcasts, in archival footage and in video games.
The cases now have about 16 individual plaintiffs, but the athletes are seeking to have the case certified as a class action on behalf of all former and present Division 1 football and men's basketball players.
The NCAA has argued in briefs submitted to Wilken that the case doesn't meet the requirements for a class action because the potential size of the class is too great and there is too much variation in the types of possible claims.
The organization also says its rules don't violate antitrust laws.
The athletes' lawyers have argued that "common questions of law and fact abound" to justify a group lawsuit on behalf of members who number "at least in the thousands."