Four more NFL head coaches were out of a job Monday morning, following two firings on the final day of the regular season, as teams that failed to make the playoffs began thinking about next season. The upheaval means that one-quarter of the league’s 32 teams now have a head-coaching vacancy.

On Monday, the ball got rolling with Marvin Lewis, the Bengals' longtime coach, telling his team that he and the Bengals had decided it was time to part ways after winning 131 games in 16 seasons as coach. In addition, the Dolphins fired Adam Gase; the Broncos fired Vance Joseph; and the Cardinals fired Steve Wilks after only one season. That brings the overall number of openings to eight, with Green Bay and Cleveland having made midseason changes.

Five of the departed coaches are African American in a league that has taken steps to improve diversity in coaching and front-office hires over the past few years. There now are two black head coaches — Anthony Lynn and Mike Tomlin. Carolina’s Ron Rivera is the only other minority head coach.

Lewis put in a word for former Cleveland coach Hue Jackson, who joined Cincinnati’s staff earlier this season after being let go by the Browns.

“I think he’s more than qualified,” Lewis Monday, via ESPN. “I think he’s been in a couple of difficult situations [in Oakland and Cleveland], and that’s tough, and it hasn’t broke his way. But I think he’s an excellent football coach, he’s a great motivator, he’s detailed. So I think he deserves an opportunity, if not here, somewhere else.”

On Sunday, the Buccaneers fired Dirk Koetter, who went 19-29 over three seasons, and shortly afterward, the Jets announced that they were parting ways with Todd Bowles, who followed a 10-6 debut in 2015 with records of 5-11, 5-11 and, following Sunday’s season-ending rout by the Patriots, 4-12. The Jets are expected to retain their general manager, Mike Maccagnan. The Bucs’ playoff drought now stands at 11 seasons, second only to the Browns, who haven’t made the postseason since 2002, while the Jets have the third-longest skid, at eight seasons.

Who’s safe?

While the Dolphins, Bengals, Jets, Broncos, Packers, Browns, Buccaneers and Cardinals are looking for new coaches, the Jaguars are standing pat.

Jacksonville owner Shad Khan announced after the team finished 5-11 with a loss to Houston that Coach Doug Marrone would be returning, along with General Manager Dave Caldwell and Tom Coughlin, the team’s vice president of football operations. He added, though, that he is “far from content with the status quo.”

These teams already had openings

The Packers and Browns fired Mike McCarthy and Hue Jackson earlier this fall, which means they’ve been taking a look around as the possibilities. Although Gregg Williams went 6-2 and is expected to interview Tuesday for the Cleveland job, he is considered a long shot. Joe Philbin has interviewed for the Green Bay job, as has former NFL coach Jim Caldwell, but ESPN reports that Northwestern’s Pat Fitzgerald is someone to keep an eye on. In addition, the Packers reportedly have asked permission to interview Patriots offensive coordinator Josh McDaniels and de facto defensive coordinator Brian Flores as well as Dan Campbell, the Saints assistant head coach and tight ends coach. The Browns also have asked to interview Campbell, while Flores also reportedly has drawn interest from the Buccaneers, Broncos and Browns.

Might the Packers consult their $134 million man, Aaron Rodgers? Fox’s Terry Bradshaw thinks that would be ill-advised. “That’d be the stupidest thing I’ve ever heard,” he said Sunday. “I would never go to a quarterback who’s only going to be with me for three more years — maybe — and say, ‘Hey, you agree with this?’ That’s ludicrous. You don’t pay any attention to what Rodgers wants. You do what’s best for your team. I don’t need to consult with him. I’m writing him a big paycheck. What I’m going to do is hire the best coach out there and he [Rodgers] is going to learn from that guy and he’s going to perform.”

Nick Saban has no NFL interest

He wouldn’t give the NFL another whirl, would he? Nah.

Nick Saban has won six college championships (with one at LSU) and his Alabama team is playing in the championship game for the fourth straight year. Naturally, this raises questions about whether he might consider a return to the NFL, with so little left to conquer on the college front. It was an especially natural question last week, when he returned to Miami, scene of his disastrous two-season NFL foray, for the semifinal game Saturday night against Oklahoma.

“I learned from my experience coming here. I learned something about myself. At the time it was a tough consequence to have to deal with,” he told reporters Thursday. “I couldn’t have been in a better situation with better people here in Miami. But I found out maybe I was a little more suited to be a college coach. That was a tough realization because of the obligations I had to the people I worked for, and the players.”

Saban left Miami after the 2006 season and the Dolphins haven’t won a playoff game since 2000.

Hot names (the non-Saban list)

Mike McCarthy reportedly turned down the chance to shop for the groceries and cook the meals with the Cardinals. He’s also believed to be a candidate in Cleveland. Though the Dolphins cut ties with him, Gase is going to be getting plenty of offers, especially from teams with quarterback talent (like the Packers, Browns and Jets). ESPN reported Monday that Gase has already heard from a majority of teams with openings, although John Elway said Gase was not a candidate for Denver’s job.

Despite the ugly way in which McDaniels dumped the Indianapolis Colts just as he was about to be introduced as head coach a year ago, things have worked out well with Frank Reich at Indy and McDaniels is likely to get another chance at a head coach position.

According to a Pro Football Talk report last week, the 4-12 Jets were interested in making a run at Jim Harbaugh, who’s making more than $7 million a year at Michigan. But Harbaugh, whose 49ers lost to his brother John and the Ravens in a Super Bowl, says he isn’t going anywhere.

“This is a choreographed message that comes up at this time every year before signing day,” Harbaugh told ESPN. “It’s people spreading messages to further their own personal agenda. But I’m on record right here, right now: I’m not going anywhere. I’m staying at Michigan.”

Because it’s never too early to think ahead, John Harbaugh’s situation in Baltimore is intriguing. Either way, he will coach the team next season, but will he choose to become a free agent and someone who would be a hot name, after that?

Who’s on deck?

There are a few attractive options among assistant coaches for NFL teams with vision. Besides McDaniels and Flores, other hot names (from The Post’s Mark Maske) include former Vikings offensive coordinator John DeFilippo, Chiefs offensive coordinator Eric Bienemy, Saints offensive coordinator Pete Carmichael Jr., Titans offensive coordinator Matt LaFleur, Rams quarterbacks coach Zac Taylor and Bears defensive coordinator Vic Fangio. The Jets reportedly are requesting permission to interview Kris Richard, the Cowboys' passing game coordinator and defensive backs coach. The Dolphins and Broncos have reportedly requested interviews with Fangio. At least four teams have requested interviews with Bienemy, according to NFL Network, including the Cardinals, Jets, Buccaneers and Dolphins.

Keep an eye on former head coaches, like Jim Caldwell (as mentioned above), who could draw interest from at least three teams, according to NFL Network. Another name to watch is that of Mike Munchak, the former Titans head coach who presently coaches the Steelers’ offensive line. The Broncos and Packers have requested permission to interview him.

One other college name to keep an eye on: Oklahoma’s Lincoln Riley.

A Falcons shake-up

Atlanta Falcons Coach Dan Quinn isn’t going anywhere, but most of his staff is looking for work. Quinn has released offensive coordinator Steve Sarkisian, defensive coordinator Marquand Manuel and special teams coach Keith Armstrong, according to ESPN.

Any surprises coming?

Well, if we knew they wouldn’t be surprises, would they? But here’s one to consider. Would the Cowboys make a change if Jason Garrett doesn’t take them deeply into the playoffs?

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