Kayvon Thibodeaux was in a New York state of mind on the eve of the NFL draft.

The Oregon defensive end left no doubt Wednesday where he is hoping to land, whether it’s with the Jets (who hold picks No. 4 and No. 10) or with the Giants (who hold picks No. 5 and No. 7). Edge rusher is near the top of both teams’ wish lists.

“That’s the biggest stage, that’s prime time,” Thibodeaux told SNY and other reporters in Las Vegas, where the draft’s first round will begin at 8 p.m. Thursday. “I’m ready. I’m excited. I don’t want to get no hopes up. I’ll be grateful to go anywhere, but that would be fun.”

The Jets and Giants both did plenty of homework on Thibodeaux, including reportedly bringing him to their New Jersey facilities for visits. The consensus No. 1 overall pick in mock drafts in October has slipped into a group of four edge rushers who could be top-10 picks, with Michigan’s Aidan Hutchinson, Georgia’s Travon Walker and Florida State’s Jermaine Johnson.

“New York is my second home,” said Thibodeaux, who was raised in Los Angeles. “It’s L.A., but it was first. It’s a different feng shui, it’s a different vibe. The people, they’re hungry. The ambition, the want-to, the drive.”

The two primary pre-draft knocks regarding the 6-foot-5, 258-pound Thibodeaux are that he might not have a true position — his best pass-rush production came on the interior line, but he is too light to play anywhere but edge in the NFL — and that he might be more interested in stardom than in football. So, why is he the right fit for New York?

“C’mon,” Thibodeaux said. “I think my business savvy is the perfect fit. I think my gregariousness is the perfect fit. I think my hunger for knowledge is the perfect fit.”

Some teams’ medical departments are concerned about a medical issue with one of Evan Neal’s legs, one source whose team kept the Alabama offensive tackle on its draft board told The Post. Sports Illustrated reported a “hip and knee” problem could affect Neal’s draft position.

Neal’s trainer Duke Manyweather called it “fake news” that some teams failed Neal on his physical and removed him from their draft boards. Neal started 40 out of 41 career games in college (missing one due to COVID-19), and he hasn’t missed an offseason workout, Manyweather wrote on Twitter.

Neal had a milder reaction than Thibodeaux on Wednesday about the potential of coming to New York.

“I’m a country boy, so the city would definitely be a new experience for me, but new experiences are great,” Neal told reporters. “I visited the Jets and Giants, but I stayed in New Jersey. It was pretty cool. It wasn’t that cold. Everybody has a funny accent.”

Another prospect the Jets and Giants could go head-to-head for is Cincinnati cornerback Ahmad “Sauce” Gardner.

His floor is considered No. 7 to the Giants, though the Eagles are seen as a potential trade-up destination if he is available at No. 6 and the Panthers want to move down.

“I feel like I’m the chosen one,” Gardner told NJ.com. “I feel like I’m the best in the draft. There’s no doubt about it.

“There’s no way I can be a bust. That shouldn’t even be an option.”

The Eagles could put together an Alabama all-star team if they draft receiver Jameson Williams to pair with DeVonta Smith in catching passes from Jalen Hurts.

“We’d be the most explosive offense in the NFL,” Williams told the Philadelphia Inquirer.

The quarterback market will be dictated by the Panthers at No. 6. The Panthers are interested in drafting Kenny Pickett, league sources said, but could gamble by trading down and hoping he slips past No. 10. That would allow the Falcons and Seahawks to have a crack at Pickett and draw in the Lions, Saints and Steelers for a trade-up situation.

The Panthers’ other options are to stick with Jets castoff Sam Darnold or maybe trade for Baker Mayfield.

“I do think we have a very good quarterback in Sam Darnold,” Panthers owner David Tepper said Wednesday.

USC receiver Drake London, who is expected to be picked long before the Chiefs are on the clock back-to-back at No. 29 and No. 30, was asked by KSHB 41 in Kansas City about potentially catching passes from Patrick Mahomes.

“That is our generation’s Tom Brady,” London said.