FLORHAM PARK, N.J. — “FitzMagic” could be here to stay if Todd Bowles gets his way. With three games still to play, the Jets coach said Tuesday that he’d like Ryan Fitzpatrick to return in 2016.

“He’s playing well,” Bowles said of the quarterback, who can become a free agent after this season. “Obviously, you deal with all of those things after the season. You like the person, you like the player.”

And the feeling is mutual. “Yeah, I’d love to be back,” said Fitzpatrick.

He did caution, however, that he’s not getting ahead of himself. “I’m focused at the task at hand,” he said, referring to the Cowboys (4-9), whom the Jets will play Saturday night in Texas. “Things change so quickly in the NFL, and so you have to take care of your business each and every week.”

Bowles said he’ll wait until after the season to discuss Fitzpatrick’s future with general manager Mike Maccagnan. “There are salary-cap issues and things involved in what we can and can’t do,’’ Bowles said. “But I make my opinion known, yes.”

So far, the Jets (8-5) have every reason to be pleased with Fitzpatrick, 33, in his first year as their starter. He needs five touchdown passes to break Vinny Testaverde’s franchise record (29) set in 1998. The Jets rank in the top 10 in points scored and points allowed. They have the second-best red-zone offense in the NFL (68.2 percent) and the No. 1 red-zone defense (33.3 percent). But more importantly, the Jets have a shot at being playoff-bound for the first time in five years.

Since trimming his trademark bushy beard, Fitzpatrick has thrown nine TDs, zero interceptions and has an average 111.5 rating in a three-game winning streak. “I’m thinking about cutting it off, see if he can get a little better,” Bowles said, laughing.

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“Nobody wants that,” Fitzpatrick joked. “I don’t want to go back to baby face. We’re going to keep it like it is.”

His transition from backup appears seamless, but Bowles said it’s been anything but smooth. “It took a lot of work,” the first-year coach said. “We’re constantly working at it, still working at it. But it’s been good that they’ve grown together.”

Teammates continue to rave about Fitzpatrick’s pocket poise, intelligence and ability. As standout receiver Brandon Marshall said: “Having a quarterback that can bring guys together and can really put guys in positions to be successful and do his job, it helps out everyone in the whole building.”

The Jets’ quarterback carousel has produced plenty of disappointing seasons recently. But in Fitzpatrick, Bowles has found someone who not only commands the huddle but also has the respect of his locker room.

“Ryan, he can make you feel at home,” Bowles said of Fitzpatrick, who was traded from Houston in exchange for a late-round draft pick in March. “He has his own humor, but he can make you feel like you want to play hard for him. He just has that persona and that personality that everybody gravitates toward.”

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But some things are out of a coach’s control.

“It’s hard with free agency and the draft to keep guys together,” Marshall said. “And I think that’s sometimes overlooked. That continuity and chemistry is really important for a locker room.”