The NCAA, which vacated Paterno's wins from 1998 to 2011, restricted the football program's recruiting abilities and barred the school from competing in bowl games, has contended the lawsuit should be thrown out.
Penn State also announced Monday it had settled with the 26 victims of former assistant coach Sandusky, who was convicted of 45 counts of sexual abuse of young boys, paying out nearly $60 million.
The NCAA has said Paterno's family has sought to place blame on the organization for his legacy being tarnished by the crimes of his assistant.
"Plaintiffs resort to tortured interpretations of the NCAA bylaws and the case law in an effort to obscure two inescapable facts: they are the wrong plaintiffs and have sued the wrong defendants," the NCAA said, in a September court filing asking for the lawsuit to be dismissed.
Judge John Leete in August set the hearing Tuesday to determine whether to move forward with the lawsuit.
Celebrity Families of 2014 [PHOTOS]