Jesperson, now 68 years old, murdered at least eight women in the United States during the early 1990s. The former truck driver is in prison in Oregon.
Heuermann is behind bars on Long Island, at the Suffolk County Correctional Facility in Riverhead.
In a video posted by the Okaloosa County (Florida) Sheriff's Office (where Jesperson admitted to having committed one of the murders), he says he wrote to Heuermann.
"Like I tried to explain to other killers who are arrested, I write to them, and I tell them how the system works," Jesperson said in the video. "When you're dealing with serial crimes, there's a difference than a single murder. You open yourself up for litigation across the board.
"You have no say in the matter, it continues, and continues, and continues. So I always try to tell people to own it. Just admit it. If you're arrested, it means the prosecutor has enough evidence to take you to court and prove you guilty. They wouldn't have arrested him if they didn't, right?"
Jesperson said he told Heuermann the same thing, and that Heuermann wrote back saying, "He'd take it under advisement."
Jesperson then rolled his eyes and laughed in the video.
In it, Heuermann complained about the food and conditions at the correctional facility.
"How is the day-to-day food - I will admit that food on SCCF (Suffolk County Correctional Facility) is not much to look forward to each day," Heuermann said. "Also yard is just walking in circles outside."
In the letter, Heuermann told Jesperson that he has been receiving numerous correspondences.
"I have gotten a number of them, asking for interviews, to be friends, pen-pals, and one guy who sent me three letters asking me to write back to add to his collection of letters," Heuermann said.
A total of 10 bodies, nine of which were women, found on the south shore of Long Island have been linked to the series of killings between 1996 and 2011.
Heuermann has pleaded not guilty to three counts of first-degree murder and three counts of second-degree murder. He's also a suspect in a fourth murder.
Heuermann was apprehended by police in midtown Manhattan on Thursday, July 13.
Police say a description and discovery of Heuermann's motor vehicle -- a Chevy Avalanche with distinct features -- as well as DNA evidence from pizza crust in a box Heuermann discarded near his Fifth Avenue office, were keys to cracking the case.
Like the 59-year-old Heuermann, Jesperson is an imposing physical presence at 6-foot-6. Heuermann is 6-foot-4.
As youngsters, both men were reportedly teased by other children for their large size.
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