Hernandez has pleaded not guilty to killing Daniel de Abreu and Safiro Furtado after a nightclub encounter.
During a hearing Tuesday in Suffolk Superior Court, Hernandez's lawyers asked Judge Jeffrey Locke to issue a gag order prohibiting anyone involved in the case from commenting outside court.
They said they were concerned Hernandez wouldn't get a fair trial because of extensive media coverage on the double slayings and another murder case against Hernandez in the 2013 death of semi-professional football player Odin Lloyd.
Prosecutors objected, saying they hadn't made any improper comments about the case.
The judge didn't immediately rule.