NEW ORLEANS — Every NFL season — as sure as there will be hand-wringing over officiating and scrutiny about whether the Jets and Giants can extricate themselves from their malaises — it happens. 

A team goes deep into the regular season without losing and the talk begins about whether that team might equal what the ’72 Dolphins did in producing a perfect, undefeated season through the Super Bowl. 

And every NFL season, a team threatening to go undefeated is beaten and members of that ’72 Dolphins team, who want their feat to stand alone, rejoice. 

The teams and the week when that first loss occurs change from year to year. But whenever it happens, former Miami players pop open champagne and celebrate. 

The Chiefs, despite their dynastic dominance in reaching a fifth Super Bowl in the past six seasons, did not go undefeated this season en route to Sunday’s Super Bowl LIX against the Eagles. They lost one regular-season game, and it came after a 9-0 start. 

But the Chiefs are in pursuit of an even more impressive feat than an undefeated regular season: a three-peat. 

A Chiefs win over the Eagles on Sunday at the Superdome would make them the first team ever to win the Lombardi Trophy three years in a row. 

That would place the Chiefs in rarefied air — New England air, to be specific. 

The Patriots and their six Super Bowl wins between 2001 and 2018 stand alone as the greatest dynasty in NFL history. A Kansas City three-peat would actually trump what those remarkable New England teams accomplished because they never won three in a row, going back-to-back once. 

And yet, as many of the former Patriots players from those teams have watched Kansas City, they stand in awe with respect and admiration for what the Chiefs are doing. 

Unlike those former Miami players, many former Patriots players want to see history made — even if it’s somewhat at their expense. 

This is proof of how impressive this Chiefs run of success has been. 

“I’m not rooting against it,’’ former New England linebacker and current ESPN analyst Tedy Bruschi told The Post. “I’m borderline cheering for it because I just want to see if it can be done. I admire and respect teams that attempt to do the impossible. I don’t think people understand how difficult it is what they’re doing.’’ 

Bruschi is not alone among his former New England teammates with that sentiment. 

“We can talk about my Patriots dynasty and how great it was, but they’re on the verge of a three-peat, something that’s never been done,’’ Damien Woody, the former New England offensive lineman and current ESPN analyst, told The Post. “If the Chiefs win this thing, they’ll have a trump card over even our Patriots dynasty as something we never accomplished.’’ 

Many of the former New England players are having flashbacks to their playing days when they watch the things the Chiefs are doing and how they’re doing them. The similarities are clear and obvious. 

“Fundamental football,’’ former Patriots тιԍнт end and current Fox analyst Rob Gronkowski said, comparing the two dynasties. “That’s what’s getting the Kansas City Chiefs all these wins. That’s what got us so many of our wins. Not making mistakes, not turning the ball over, finding mismatches.’’ 

Then Gronkowski added with a mischievous smile: “Having great coaches, having a great quarterback … and having a great тιԍнт end.’’ 

Woody spoke of the “many parallels’’ between the respective runs of the Patriots and Chiefs. 

“Both teams understand about playing in the moment,’’ Woody said. “They don’t get beyond themselves. It’s all about the next meeting, the next practice, the next game. They don’t talk about the Super Bowl and, ‘We want to do this.’ No, they’re just all about process, process, process. 

“I remember when I was in New England, that’s what Bill [Belichick] preached all the time. It was about the process. It always felt like you were in a dark tunnel, and the only time you got out of that dark tunnel was when the confetti was dropping on your head [after a Super Bowl victory]. That’s when you finally felt the reward for that grind that you went through throughout the season.’’ 

Chiefs offensive lineman Joe Thuney, who won two Super Bowls while playing in New England before joining the Chiefs, called the common denominator between the two dynasties “a selfless atmosphere.’’ 

“Guys are sacrificing things for the benefit of the team even though it might not be best for them individually,’’ Thuney told The Post. “It’s just that communal effort with everyone pulling in the same direction, trying to win — regardless of how it gets done. That’s been a very common theme for both teams.’’ 

Bruschi sees the same DNA in these Chiefs teams and those Patriots teams, citing the Chiefs’ uncanny ability to keep winning close games when they don’t have their “A” game. 

“In 2007, we dominated a lot of people,’’ Bruschi said. “But ’03 and ’04, we had a lot of similar games to [the Chiefs] in terms of winning and then teams leaving the field talking to themselves, thinking, ‘They weren’t that good. How did they just beat us?’ 

“That’s what a lot of the teams thought about Kansas City this year. But really, they just got beat by a better team.’’ 

Bruschi sees Kansas City winning the same way New England did, by owning the clutch moments, very much like the great tennis players have a knack for winning the points in the biggest moments of the match. 

“We knew what other teams didn’t, which was when the situation came where a winning play had to be made, we knew exactly how to do that,’’ he said. “It was borderline arrogance to just having the knowledge and experience of, ‘We know where this game’s going to go and we’re ready for it.’ ’’ 

The Chiefs, who have won an NFL record 17 consecutive games decided by one score, are always ready when they have to be. That’s their collective superpower. 

They, too, are constantly ready when injuries or player departures threaten to set them off course, which is an area that former Patriots receiver and current Fox analyst Julian Edelman said is a tie that binds the two dynastic franchises. 

“The similarities are the ability to evolve your team each and every year,’’ Edelman said. “You’re never the same team from year to year. Another huge parallel is they have Patrick Mahomes and we had Tom Brady. They’ve also changed their idenтιтy from being a Sєxy, high-flying, Tyreek Hill-throwing team to a team that plays situational football. That’s what we did in that whole transition from the 2007 era to the second run of Super Bowls.’’ 

Asked if he, like Bruschi, is rooting to see a three-peat, Edelman said, “I’m not rooting for anybody, but I’m not going to be a hater. I think it’s an unbelievable feat and they’ll go down as probably the best team of all time if they can do it.’’ 

Woody took it a step further. 

“I think they’re already the greatest dynasty,’’ he said. “The Patriots actually had two dynasties if you think about it, because they won three and then they went a decade without winning a Super Bowl and then they won three more. What the Chiefs are doing right now, seven straight conference championships, and if they win this Super Bowl, it’ll be four in six years. 

“That’s crazy.’’