DiMaggio is accused of kidnapping Anderson and murdering her mother and Ethan.
The family suspects that the DiMaggio might be the victims' biological father.
"We are going to be requesting from the Anderson family that we try to get DNA samples from Hannah. And if they have anything left from Ethan, that we get a DNA sample," family spokesman Andrew Spanswick said.
"There has been a lot of rumors that Jim might be the father of either or both children."
Spanswick said DiMaggio's sister Lora made the request, saying that she already had DNA samples of her brother.
This comes after Lora DiMaggio was removed as a beneficiary of her brother's life insurance policy. Instead, James DiMaggio changed it to benefit Hannah Anderson's paternal grandmother Bernice.
A representative of the Anderson family shot down the theory.
"Brett and Tina Anderson did not meet Mr. DiMaggio until the sixth month of Tina's pregnancy with Hannah. Brett Anderson's DNA was used to identify the body of his dead son Ethan Anderson," the family statement said.