The NFL wants the complaints handled in arbitration, not in court.
Lawyers for more than 4,200 players say in their lawsuits that the league hid the known risks of concussions and rushed players back into the game.
Senior U.S. District Judge Anita Brody says she expects to issue her ruling July 22 on whether the lawsuits can go forward.
Brody heard brief arguments in early April from a pair of nationally prominent lawyers, David Frederick for the players and Paul Clement for the league.
Many former players say they suffer from dementia, Alzheimer's disease and other neurological conditions and believe that they stem from on-field concussions.