PHOENIX — Josh McCown may be the new quarterback on the roster, but that doesn’t necessarily mean he’s the Jets starter.

Speaking at the NFL’s annual meeting on Tuesday, coach Todd Bowles made it clear that there will be “heavy competition” between McCown and young incumbents Christian Hackenberg and Bryce Petty.

That might come as a shock to some, considering the one-year, fully guaranteed, $6-million deal the organization gave the 37-year-old McCown last week. But Bowles insisted that the competition will be wide open when players report for their offseason program, adding: “Nobody has been promised the starting quarterback job.”

And, according to Bowles, how each quarterback fares in training camp will determine which one gets the green light.

“Hack’s going to get a chance to play. Bryce will get a chance to play. Josh will get a chance to play,” the third-year coach said. “It will be good competition there, and everybody knows that. We’ll see going forward from there.”

That’s sure to be welcome news for Hackenberg, who essentially had a redshirt season as a rookie and did not take a snap during a regular-season game.

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But the quarterback competition at 1 Jets Drive also could include another candidate.

Peppered with questions about the Jets’ most important position, Bowles didn’t rule out drafting another quarterback or keeping four on the roster as they did last season with Petty, Hackenberg, former starter Ryan Fitzpatrick and backup Geno Smith. He did say, however, that the Jets are set with McCown being the only veteran in the quarterback room.

But Bowles said “there is a scenario” where the organization could draft another quarterback at No. 6 overall in the draft — and that prospect would have a chance to earn the starting job as well.

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“You never say never,” the coach said.

The Jets have shown interest in several top quarterback prospects, including Mitchell Trubisky (North Carolina) and Deshaun Watson (Clemson). But that doesn’t mean they’ve given up on Hackenberg, their 2016 second-round pick.

“You hope Hack gets better and is going to come back with a new attitude,” Bowles said, later clarifying that the youngster’s attitude wasn’t poor, but rather Hackenberg has to adjust his mindset to being in contention for the starting job. “You want him to play better right from that standpoint. It’s not going to stop us from drafting a quarterback. Hack’s not afraid of competition and nobody else on the roster needs to be afraid of competition. If you are, you’re in the wrong business.

“His attitude was great last year,” Bowles said of the former Penn State quarterback. “We just knew we were redshirting him and he wasn’t playing, so this year he has a chance to play, he’ll have some pep in his step.”

One thing that could complicate matters is the health of Petty, who underwent surgery in January to repair a torn labrum in his non-throwing shoulder. It’s unclear when he’ll return (organized team activities begin May 23).

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Regardless of who is under center in Week 1, it’s obvious Bowles is expecting his quarterback to do one thing: be an efficient game manager.

“We just have to make sure we have a guy that doesn’t turn the ball over,” he said, “and we have a guy that can manage the room, and make sure we help that guy and not put it solely on the quarterback.”

Notes & quotes: The Jets announced the signing of former Colts offensive lineman Jonotthan Harrison. According to a source, it’s a one-year deal for the versatile Harrison, who will compete for the starting center spot.