The Orlando (Fla.) Sentinel reported the content of Peterson's letters was not clear.
Peterson was convicted three years ago of killing his wife Laci and unborn son, Conner. He was sentenced to death in 2005.
Anthony is accused of killing her daughter Caylee Marie Anthony. She was charged with first-degree murder this month. The child's body has not been found.
Anthony has not been corresponding with Peterson, said a spokesman for her attorney, Jose Baez, who screens his client's mail.
Celebrity Families of 2014 [PHOTOS]