But Nelson said he did not interpret it as an actual threat to his safety. Nelson would not say what Jones said to him, but he said the media reports about Jones' remarks were accurate.
The New York Daily News reported that Jones told Nelson that he was "going to find out where you live and come and get you" during the Bengals' 49-9 win over the Jets on Sunday.
"I wouldn't say it was a threat. I'm not going to say that he threatened me or anything like that," Nelson said on a conference call. "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."
Jones also got into a verbal scuffle with Jets coach Rex Ryan. The veteran cornerback told the Bengals' website that Ryan told him to "shut the hell up." Ryan said he did not remember what he said to Jones.
"Sometimes you have conversations with guys and all that stuff, but I don't recall having it," Ryan said. "I've always liked him. Again, I guess it's a possibility, but I just don't remember it."
Jones, who has had legal issues, was unhappy with Nelson's play Sunday, telling the Bengals' website that the Jets wide receiver played "dirty" and cut him about four times.
Jones, who returned an interception for a touchdown, said he hoped Nelson will get fined, as he believed Nelson hit him with three "cheap shots" at the end of plays. Nelson was flagged once for unnecessary roughness for sideswiping Jones.
Nelson defended himself by saying he's a physical player from whistle to whistle and that he did not believe his hit on Jones was a dirty play.
"I've never had anyone call me dirty ever in my life before, so this was just an incident where I just think he apparently wasn't fond of playing against a physical receiver from the beginning of the game to late in the game," Nelson said. "His view of dirty is a little bit different than mine.
"I wasn't doing anything outside the rule book; I wasn't doing anything that I haven't done before. I cut him one time in the entire game. Never hit him late. ... For him to call me dirty I think is inaccurate and not true."
Nelson said he isn't viewing Jones' comment as a threat because he believes it was something said in the heat of the moment. That comment, though, did stand out from others Nelson has heard.
"In the heat of the game, in the heat of battle, I've heard a lot of crazy stuff said," Nelson 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."
Ryan, like Nelson, did not believe the receiver played dirty against the Bengals. Nelson, who just signed with the Jets this month, led the Jets with eight catches for 80 yards Sunday.
"I thought he was playing hard. He was blocking like crazy, and I think that's maybe what Pacman took offense to that, but he was competing his butt off out there," Ryan said. "I was impressed with him. I never thought it was a clip, the one he got flagged on. I thought it a clean shot."