Jets RB Dalvin Cook runs during training camp at the Atlanic Health...

Jets RB Dalvin Cook runs during training camp at the Atlanic Health Jets Training Center in Florham Park, N.J., on Aug. 17. Credit: Patrick E. McCarthy

FLORHAM PARK, N.J. — Robert Saleh thought the Jets had zero chance of signing Dalvin Cook after their July meeting with the Pro Bowl running back.

Saleh revealed Saturday that they presented a “worst-case scenario” to Cook about his role. According to Saleh, he told Cook he could be watching from the sideline if Aaron Rodgers is rolling in the passing game or Breece Hall has the hot hand running the ball.

“When he left, I was like, ‘There’s no way after that he’s going to want to play here,’  ” Saleh said. “It was laid out exactly. I was like, ‘Why would he want to be here the way we explained it?’  ”

It could have been a test to see how committed Cook would be after spending the last six years in Minnesota (in his last five full seasons as a starter, he averaged 24.1 touches and 112.7 rushing yards per game). When Cook remained interested in playing for the Jets, Saleh concluded they had to sign him.

“To his credit, he’s like, ‘Coach, I just want to win,’  ” Saleh said. “So when he left and their team still showed interest, I was like, ‘Absolutely bring him in; he’s only going to help us.’    

“He is all-in,” Saleh added. “It gives us faith that he is all-in on this process. He’s ready to do anything that we need to do to win football games whether it’s 25 carries, whether it’s one carry. Whatever it is. He’s ready to roll.”

The Jets signed Cook, 28, in mid-August to a one-year deal. He was viewed as insurance for Hall, who is returning from an ACL tear. Cook could be much more than that, particularly early on this season.

Both backs are scheduled to play Monday night when the Jets open against the Bills, but Cook may be featured more. As Hall gains more strength and confidence in his knee, he is expected to take over as lead back.

“It’s a normal show for me,” Cook said. “I expect the same thing every year, be productive. I ain’t worried about carries and all of that. I just want to win a football game and have some fun.”

Hall said he feels great and is good to go, but Saleh said the Jets will be “smart” with how he is used. He is such a big part of the Jets’ present and future and was on his way to being named Offensive Rookie of the Year before suffering the injury in the first half of Week 7 at Denver.

Cook has proved how explosive and productive he can be. It’s a luxury that the Jets have someone like him to be their option 1A in the backfield. He has made the Pro Bowl the past four seasons and rushed for at least 1,135 yards in each of those seasons, with 43 total touchdowns.

“Glad we got him,” Saleh said. “He is a special person. He’s got a special mindset to him.”

Offensive coordinator Nathaniel Hackett echoed those sentiments. Hackett said he didn’t know Cook before he came in for that first meeting and that he quickly made an impression.

“I was just so impressed with how he communicated, his presence, and then to now get him out on the field and watch his work ethic has been something great to see,” Hackett said. “It is great for all of the guys.”

The transition has been relatively seamless for Cook. He wanted to play with Rodgers, he worked in a similar offense in Minnesota and he’s grown close with Hall.

“I’m a part of a great group right now,” Cook said. “I’m looking forward to go win a bunch of games with these guys.”

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