On NFL Network's Good Morning Football on Thursday, Jennings was asked if he could see the writing on the wall in the Big Apple.
"Well, I mean, could I see it coming? You always have that possibility," he said. "You could kind of see a rotation in the backfield and how we were operating that that was a possibility that could be strong. Obviously, I'm a vet in the game and I kind of see it from the business standpoint.
"But where I'm at right now, I'm excited, you know? Free agent, you know, healthy. I'm down in Florida already training, trying to get ready for a team to call me. I always say my job every single year is to make one GM right and that's no doubt what I'll be doing this upcoming season."
Jennings started 12 of 13 games played in 2016 but had his snaps heavily cut into by Paul Perkins, especially down the stretch when the team began to trust the rookie more. Jennings compiled just 593 yards last season, but earned a miserable 3.3 yards per carry average. He never topped 875 yards in three seasons with the Giants. Cutting Jennings saved Big Blue $2.5 million in salary-cap space.
After being selected in the seventh round in 2009 by the Jaguars, Jennings has been a career committee back in Jacksonville, Oakland and New York. Turning 32 next month, Jennings said he still believes he can play, even if some doubters believe his eight-year pro career is over.
"Everybody's going to have opinions," he said. "You've got a lot of people from the couch that have ideas, the Twitter world, Instagram and social media. But for me, I have to be able to look into the mirror every day. I've got a family that stays on my tail and it's for the people who love me. The people that stick with me. I stay motivated, and anybody that are haters, it doesn't make a difference. I don't hear those."
Jennings added that he's hungry to prove he still has gas left in the tank.
"I've got a chip on my shoulder," he said. "And when you have a chip on your shoulder and you got the work ethic and you combine those two, you're going to be successful."
Over the 30-year-old barrier, Jennings will have to wait out the market before landing in an ideal spot. With the NFL draft deep at the running back position this year, many teams are likely to go with younger, cheaper talent. Even at 32, Jennings won't have as many carries on his tires as other backs his age and could provide a veteran backup in the right situation.