Hernandez's lawyers say in court filings released Friday that it is "reasonable, appropriate and humane" that his closest family members be permitted to attend.
Prosecutors have said they may call his mother, Terri Hernandez, or fiancee, Shayanna Jenkins.
Hernandez's lawyers say both women testified before a grand jury in the case and there's no reason to think their trial testimony would be influenced by what other witnesses say.
Jury selection is due to start Jan. 9.
Jenkins has been charged with perjury in the case and has pleaded not guilty.