Clemson's Deshaun Watson warms up before the NCAA college football...

Clemson's Deshaun Watson warms up before the NCAA college football playoff championship game against Alabama Monday, Jan. 9, 2017, in Tampa, Fla. Credit: AP / Chris O'Meara

INDIANAPOLIS — The Jets have spent two second-round picks and a fourth-rounder on quarterbacks since 2013, but they may still be in the market for a high-round pick in this year’s draft.

Same with the Giants, who have Eli Manning under contract for the two seasons, but publicly acknowledged after the season that it’s time they at least start looking for a successor to their 36-year-old starter.

While there’s no guarantee they’ll take a quarterback with the sixth overall pick, the Jets are covering their bases by meeting with all the top prospects in this year’s draft. That list includes Mitch Trubisky of North Carolina, Deshaun Watson of Clemson, Notre Dame’s DeShone Kizer, and Patrick Mahomes of Texas Tech.

The Giants, who have the 23rd overall pick, are also expected to meet with the top quarterback prospects. And they have already interviewed the draft’s top two tight ends — Alabama’s O.J. Howard and David Njoku of Miami.

The Jets have plenty of needs at several positions other than quarterback, and there’s increasing speculation they’ll make a run at Bucs free agent quarterback Mike Glennon. But they’re still interested in getting a read on the blue chip prospects at the top of the draft board.

“If the Jets decide to select me, I’m cool with it,” said Watson, who won the national championship with a spectacular comeback win over Alabama. “It would be a great opportunity for me to go up there and perform and build a career and build a name for myself.”

But Watson would also be content to sit for a year or two, a scenario that would likely come into play with the Giants, given the fact that Manning hasn’t missed a start since taking over the No. 1 job halfway through his rookie season in 2004. Giants general manager Jerry Reese acknowledged publicly for the first time the day after the team’s wild card playoff loss to the Packers that the team needed to find an eventual replacement for Manning.

“I wouldn’t mind that,” Watson said of initially being a backup. “Any situation, I’d respond to it. Learn from a veteran guy and watch how he works. I can sit there and learn, build my game and become a better player. If it happens, it happens, but it wouldn’t be a factor for me.”

The top of the draft is filled with quarterback-needy teams, as the Browns at No. 1, the 49ers at No. 2 and the Bears at No. 3 are all in the market for new quarterbacks. There is a wide disparity of opinion on whether some — or even any — of this year’s top prospects merits top 10 consideration. But in a league where quarterback play is at a premium, teams invariably overdraft when it comes to gambling on a young passer.

The Jets may have been guilty of overvaluing Christian Hackenberg, their second-round pick last year. He didn’t get close to playing in a game, despite the fact the Jets finished 5-11 and played meaningless games down the stretch. Bryce Petty, a fourth-round pick in 2015, got some valuable playing time before suffering a shoulder injury against the Patriots in December, but he struggled with turnovers in his limited action.

Geno Smith, the Jets’ second-round pick in 2013, suffered a torn knee ligament in his only action after replacing the ineffective Ryan Fitzpatrick, and he has not ruled out returning to the team now that his rookie contract has expired.

But the Jets are still covering their bases on closely studying this year’s draft-eligible quarterbacks.

“There’s going to be pressure everywhere you go, but there’s no more pressure than what I put on myself,” said Trubisky, who had only one year as a starter before coming into the draft. “I’m going to be excited wherever I go. I feel like I’ve meshed well with a lot of coaches. I’m trying to talk to as many coaches as possible. Even if they might not be selecting a quarterback high, I love the game and love talking ball.”

Trubisky doesn’t look at his limited experience as a starter as a deterrent.

“I have only 13 starts, but I’ve played in 30 games, and I’ve come off the bench,” he said. “I’ve seen significant time. I’m a student of the game, and I’ve seen a lot of defenses. I feel like I’m in a really good spot to take my game to the next level. I feel really confident. I feel like I have the tools to be successful in the NFL, so whatever organization selects me, I’m going to try to compete and learn the system as fast as I can.”

Mahomes is one of the more intriguing prospects this season. He may have the strongest arm of anyone, but playing in Kliff Kingsbury’s “Air Raid” offense at Texas Tech may require more of an adjustment to the pro game. Kingsbury, the former Texas A & M offensive coordinator who helped develop Johnny Manziel, does not have his quarterback make any reads.

“Wherever I go, I’m going to learn from Day One,” said Mahomes, the son of former Major League pitcher Pat Mahomes. The younger Mahomes was considered a major league prospect himself before choosing to concentrate on football. “I’ve worked on holding the ball higher and perfecting my footwork in the pocket. It’s something you have to keep working at before it becomes habit. I still have a long way to go.”

The Jets also have their eye on Cooper Rush of Central Michigan.

“I spoke to Jeremy Bates, the quarterbacks coach (of the Jets),” Rush said. “They threw out a few plays that I liked, kind of what they saw in me, what I have to work on.”

In the end, neither the Jets nor Giants might take a quarterback. But given both teams’ close scrutiny of the top prospects at this week’s combine, it won’t be a surprise if they both come away with a player they consider their quarterback of the future.

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