In that unsolved crime, the victims died after taking Extra-Strength Tylenol capsules bought in drug stores and groceries that had been laced with potassium cyanide.
Kaczynski, 69, who is serving a life sentence in Florence, Colo., said in documents filed in federal court in Sacramento, Calif., that "the FBI wanted a sample of my DNA to compare with some partial DNA profiles connected with a 1982 event in which someone put potassium cyanide in Tylenol," McClatchy/Tribune News reported Thursday.
James Lewis, who wrote letters to Tylenol demanding $1 million to stop the killings, has been the prime suspect in the case.
Although he served a 13-year sentence for extortion he has never been charged with murder.
Kaczynski made the claim of an FBI investigation in a letter filed last week in an attempt to stop a federal auction of his possessions, including his handwritten manifesto and his hoodie and sunglasses.
The items were seized in 1996 from Kaczynski's cabin in the Montana woods where he planned an 18-year bombing campaign that killed three people and injured 23 others around the country.
Kaczynski said some of the possessions could prove his whereabouts and activities in 1982.
FBI officials did not responded to a request for comment.