In confirming reports that the Jets and Cowboys had discussed a deal this summer involving a swap of Micah Parsons and Quinnen Williams, Jerry Jones either revealed the Jets once had a wildly appealing trade on the table or, more likely, misremembered or embellished the details of that deal.

During an appearance on 105.3 The Fan in Dallas on Thursday, the Cowboys owner said he attempted to swing a trade for Williams during training camp and offered Parsons plus a first-round pick to the Jets. According to Jones, the Jets did not have the cap room necessary to bring in and extend Parsons, so the deal never was consummated.

The more likely trade discussions — which Jones had referred to on ESPN Radio in September — involved the Jets attaching a draft pick with Williams rather than the Cowboys adding a pick with Parsons.

Quinnen Williams has played well for the Cowboys. IMAGN IMAGES via Reuters Connect

Jerry Jones may have fibbed on this offer. Stephen R. Sylvanie-Imagn Images

The point that Jones was trying to get across, in either case: “I thought that much of Williams, and he’s showing you what he can do for a defense.”

In the end, the Cowboys acquired Williams earlier this month for a 2027 first-round pick, 2026 second-round pick and defensive tackle Mazi Smith.

Parsons fetched the Cowboys two first-round picks plus Kenny Clark, which is much more in line with a return for a superstar pass rusher. Parsons has notched 12.5 sacks in his first 12 games with the Packers.

Since coming over from the Jets, Williams has helped lead a midseason revival for a Cowboys team that once seemed dead to rights. Dallas is 6-5-1 after its third straight win Thursday — all with Williams — a 31-28 win over the reigning AFC champion Chiefs on the heels of a 21-point rally to down the Eagles the previous week.

The Cowboys sent Micah Parsons to the Packers. IMAGN IMAGES via Reuters Connect

Running back Braelon Allen, who injured his knee in Week 4, is likely done for the season, Jets coach Aaron Glenn said.

Added to the injury report is CB Jarvis Brownlee Jr., who is questionable for Sunday’s game against the Falcons with a hip injury. He did not practice Thursday.

Guard Joe Tippmann returned to practice after sitting out Wednesday with a personal issue. Defensive tackle Harrison Phillips (foot), who fully practiced after being a limited participant Wednesday, is questionable for Sunday.

Defensive coordinator Steve Wilks on a historic defense that has forced one turnover in 11 games: “I asked the coaches and players, ‘Which one of you guys aren’t living right?’ ” he joked before referring to the Ravens’ five turnovers against the Bengals. “Because I see the game [Thursday] night and they got five, I believe it was, and that’s the most. So, we know they come in bunches, and we’re going to continue to coach it.

“In all seriousness, and we’re going to continue to emphasize it in practice and I think our guys have been doing a great job, I know they have, of really trying to execute that. And then we have to have that intent once we get into the game and really trying to go for the football.I’m expecting, hopefully, they are going to come soon, and hopefully this Sunday.”