On the surface, it looks like the Jets are playing a high-stakes game of chicken with their quarterback position.

Particularly for the experienced Jets fan who’s become programmed to expect the worst, it appears to have the potential to blow up and leave everyone disappointed.

Derek Carr, the Raiders former quarterback who’s now a free agent, this past weekend visited Jets brass — general manager Joe Douglas and head coach Robert Saleh. The visit, over a proper Italian lunch at Fiorino Ristorante in Summit, N.J., reportedly went well.

As Carr and the Jets dined on pasta, Aaron Rodgers — quite likely the Jets’ first choice as their quarterback for the next year or two — embarked on his “darkness retreat’’ to try to sort out his future. Here’s where this thing gets complicated: Rodgers, whom the Packers are ready to move on from, according to some reports, has not said whether he wants to retire or continue playing and which team he’d like to play for. The timetable for Rodgers’ and the Packers’ decisions is murky.

The assumption — hope, really — is the Jets, through back-channel intel, already have a decent idea about Rodgers’ intentions.

They’re certainly equipped to have a decent idea.

First,, it would make some sense to think newly hired Jets offensive coordinator Nathaniel Hackett — who is close to Rodgers after Hackett was the offensive coordinator in Green Bay from 2019 to 2021 — has some idea about what Rodgers’ plans might be.

Also, Saleh and Packers head coach Matt LaFleur are best friends, so it’s difficult to imagine the two haven’t had private conversations about whether or not the Packers want Rodgers to return. (Tampering, of course, is prohibited by the NFL, but with the endless chain of personal relationships around the league, tampering in some shape takes place all around the league.)

The Jets have reportedly reached out to the Packers to express their interest in trading for Rodgers.

If the Jets are as in the dark as Rodgers was on his “retreat,’’ they’re in jeopardy of missing out on both Rodgers (should he opt to retire, stay in Green Bay or play for a different team) and Carr, who has interest from other teams, including the Saints, the other team he has visited.

And if they wait too long for Rodgers, the Jets again face the possibility of missing out on Carr if he decides to sign elsewhere. The last thing the Jets want is to be the team standing without a quarterback when the music stops.

Assuming Rodgers and Carr are the two quarterbacks the Jets have narrowed their search to, here’s a look at the pros and cons of each player’s fit in Jets green and white.

What’s the plan: Long term or short term?

If the Jets think they’re truly a quarterback away from winning a Super Bowl, Rodgers is their man over Carr.

Rodgers is one of the most prolific, winningest quarterbacks in NFL history, compiling a 147-75-1 regular-season record and going to the playoffs 11 times as a starter, playing in 21 postseason games and winning one Super Bowl.

Carr, in his nine NFL seasons, has a suspect 63-79 record and has played in only one postseason game, after the 2021 season.

Statistically, Rodgers is the superior quarterback, throwing 475 career TD passes to just 105 INTs with a career 103.6 quarterback rating; Carr has thrown 217 TDs to 99 INTs with a career 91.8 rating. Rodgers is a four-time MVP, the last two coming in 2020 and 2021.

So, if the Jets think they can compete for a Lombardi Trophy with their defense, ranked fourth in the league in 2022, and offensive skill-position talent, Rodgers is their man.

If they want to sign the player who’ll be around for the next five-plus years, Carr may be a better choice at age 31 (he’ll be 32 in March) to Rodgers’ 39. Rodgers would be with the Jets for 2023 and maybe 2024.

Carr could be much more of a long-term solution. Rodgers would be a one or two-year rental.

At what cost?

Carr is a free agent, and can be signed to a reasonable contract. Rodgers is entering the second year of a $150 million guaranteed contract and is Packers property. That means it’s going to cost the Jets at minimum their first-round pick (13th overall) in April’s draft and then some to acquire Rodgers. Then they’d have to do something about reworking his unwieldy contract.

Commitment

There’s some question about how all-in Rodgers remains at this point in his career. He’s coming off one of the worst statistical seasons of his career — his 12 INTs were his most since his first full season in 2008.

It takes a lot of energy to start new with another team, especially when you’ve played your entire career in the same place. This could be a deterrent for Rodgers.

Carr has to be the hungrier player, having never won before and with a chip on his shoulder after having been shunned by the Raiders, the only team for which he’s ever played.

Carr could duplicate with the Jets what Matthew Stafford did two years ago when he left the Lions for the Rams and won a Super Bowl. Stafford, like Carr, was considered by many as a statistics compiler who played on subpar teams.

How does Zach Wilson fit in?

Saleh and Douglas have told anyone who’ll listen that they haven’t given up on the 2021 first-round draft pick, who’s failed to develop the way a No. 2 overall pick is supposed to in his first two seasons.

If Rodgers is the quarterback the Jets bring in, that would give Wilson a year or two to watch and learn from one of the all-time greats. Though Rodgers doesn’t come across as the mentoring type, he appeared to take a liking to Wilson after the two met during summer scrimmage session in Green Bay in 2021.

If Carr is the Jets’ next quarterback, he surely isn’t signing to be a placeholder for Wilson. Carr would be here for a longer haul, and presumably that would stunt Wilson’s eventual development into a starter if that’s the plan.

Who’s the best fit?

In Hackett’s three seasons as the Packers offensive coordinator, Rodgers won 13 games each year, collected two MVP awards and threw 111 TDs to just 13 INTs.

The Jets also recently hired Todd Downing as passing-game coordinator. Downing was on the Raiders’ staff for Carr’s Pro Bowl seasons of 2015, 2016 and 2017. Carr threw a career-high 32 TDs in 2015 and a career-low six INTs in 2016.

Between the two quarterbacks, Rodgers is much more equipped to play in cold Northeast weather than Carr. In 10 career games played in 40 degrees or colder, Carr has a 3-7 record with 11 TDs, 12 INTs, a 57 percent completion rate and a 69.2 passer rating.

Rodgers, because of his experience as the higher-profile superstar, likely would handle the New York market better than Carr, who hasn’t been exposed to nearly as much media scrutiny as Rodgers. The quirky Rodgers would provide added entertainment value should he come to New York.

What do Douglas and his scouts have in store for an encore as this year’s draft approaches?

They have quite an act to follow.

Douglas and his staff delivered one of the best draft classes in franchise history last year when they selected cornerback Sauce Gardner and receiver Garrett Wilson, who won the NFL’s Defensive and Offensive Rookie of the Year honors, respectively.

Also in that draft were running back Breece Hall, who was on his way to a possible rookie of the year season before he injured his knee in October, and edge rusher Jermaine Johnson, who was productive in the defensive line rotation and on special teams.

With the NFL Combine taking place next week in Indianapolis, the Jets surely will be focusing on offensive line help. It would be stunning if the Jets don’t use their 13th overall pick on a tackle (unless they’ve traded it away for Rodgers).

Since Douglas took over in 2019, the Jets have allowed the fourth-most sacks in the league (190). Left tackle Mekhi Becton, Douglas’ 2020 first-round pick (No. 11 overall), has missed the past two seasons due to knee issues. And both tackle positions were revolving doors last season because of injuries.

Expect the group of players they’ll thoroughly evaluate and interview next week in Indy to include the top tackles: Ohio State’s Paris Johnson Jr., Northwestern’s Peter Skoronski, Georgia’s Broderick Jones, Maryland’s Jaelyn Duncan, Ohio State’s Dawand Jones, Syracuse’s Matthew Bergeron and Tennessee’s Darnell Wright.

Another position of need for the Jets is safety. Neither Lamarcus Joyner nor free-agent pickup Jordan Whitehead distinguished themselves last season. If the Jets pick one in the first round, a name to watch would be Alabama’s Brian Branch, who also can play nickel cornerback. Players who’ll be available later include Texas A&M’s Antonio Johnson, Notre Dame’s Brandon Joseph and Alabama’s Jordan Battle.

At receiver, the Jets could part ways with veteran Corey Davis and Braxton Berrios. The draft options at the position include Tennessee speedster Jalin Hyatt, Boston College’s dynamic slot receiver Jay Flowers or Cincinnati’s versatile Tyler Scott and Michigan State’s Jayden Reed, who is not only a vertical threat receiver but a punt returner.