Jones reportedly told Nelson that he was "going to find out where you live and come and get you" during the Bengals' 49-9 win after becoming unhappy with what he described as "dirty" play by the former Buffalo Bills player.
Nelson would not confirm exactly what was said but believes that the comment was merely one made in the heat of the moment by a frustrated Jones.
"I wouldn't say it was a threat. I'm not going to say that he threatened me or anything like that. He did say some stuff on the field, but I wouldn't take it as a threat. I'm not going to get into specifics of exactly what he said. But I can confirm I've read a lot of reports that are true," Nelson told reporters.
"In the heat of the game, in the heat of battle, I've heard a lot of crazy stuff said. Never to that point. At the same time, it was in the battle of the game, it was never repeated, he didn't say it again. At the end of the game, he didn't come up to me and say anything, either.
"It was just one of those things where I guess he was extremely frustrated or extremely irritated at one point in the game and just said it in the heat of the game. I didn't take it anything further than that one play."
The Jets are currently second in the AFC East with a 4-4 record and will face the New Orleans Saints on Sunday.