The Ryan Fitzpatrick saga has taken another unexpected turn.

The quarterback, who has been engaged in a contract logjam with the Jets since free agency began, reportedly is threatening to sit out the 2016 season and beyond.

“There’s a lot of chatter out there that he’d rather retire than come back and play for the offer that they have on the table,” ESPN’s Adam Schefter said on air Thursday afternoon, just hours before the NFL Draft.

Fitzpatrick’s agent, Jimmy Sexton, could not be reached for comment.

Fitzpatrick, who will turn 34 in November, has been seeking a multiyear deal comparable to the going rate for starting quarterbacks — somewhere in the range of $14 million to $18 million. The Jets, however, have no interest in paying him that much.

Their initial offer, according to a source, was about $7 million. It’s unclear how many counter- offers the Jets have made since then.

Fitzpatrick remains their top choice, but the Jets also have had an eye on other quarterback options this offseason, wining and dining free agents Robert Griffin III and Brian Hoyer in the past month. Each quarterback met with members of the front office and coaches during a two-day visit but left the facility without an offer.

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Griffin, who was released by the Redskins on March 7, signed with the Browns on March 24. Hoyer traveled to Denver after his meeting with the Jets, but the Broncos didn’t offer him a deal, either.

Regardless of what happens during the draft, the Jets’ top priority remains re-signing Fitzpatrick. Despite the rumors that he either will retire or sit out the upcoming season, they plan to resume contract talks with him after the draft.

“We like Ryan very much,” general manager Mike Maccagnan said at his pre-draft sit-down with reporters. “We feel like we have a very good situation for Ryan here. He’s a very good fit for us, too. So hopefully at some point in time, we can work out some kind of an agreement on a contract.

“ . . . This is going to be a fluid process,” he added. “We’re trying to do everything within our power to re-sign the players we’d like to re-sign . . . and try to do something that will hopefully facilitate a deal, but it may take some time.”

The Jets have backups Geno Smith (their 2013 and ’14 starter) and Bryce Petty on the roster, but it’s clear that they want an experienced veteran as a placeholder before they hand over the offense to a quarterback of the future (whoever he may be).

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Fitzpatrick, who was traded from the Texans in March 2015, quickly became a locker-room favorite. He threw a franchise- record 31 touchdown passes and had a career-high 3,905 passing yards last season en route to leading the Jets to a 10-6 record, one win shy of the playoffs.

His reunion with offensive coordinator Chan Gailey made all the difference in Fitzpatrick’s career resurgence. But he also had a few forgettable games, including two-pick performances against Buffalo and Houston in back-to-back weeks and three fourth-quarter interceptions against the Bills in the Jets’ win-and-in game in the regular-season finale.

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