The one-year contract buys the Rangers time to see what they have in some of their younger players before deciding whether to make a long-term commitment to Hayes.
"In a perfect world, Kevin Hayes is here after one more year and we keep going with him. Everything goes the way he wants it to and we do," Gorton said. "We certainly have (the NHL salary cap) room to keep him and move forward, it's just a matter of the contract. As we went through the process, the one-year deal seemed to be the best fit for what we're doing right now. I think Kevin was comfortable saying, 'OK, I'll come back this year and I'll do exactly what I say I'm going to do, and then let's talk.' We're comfortable with that too."
Hayes said he believes he'll prove to the Rangers he can be a vocal leader on and off the ice.
"It's my fifth year and I think it's time," Hayes said.
He also said he thinks new coach David Quinn's up-tempo style will help him add offense to his game, but it doesn't mean he'll have to sacrifice his role as New York's top shutdown center.
Last season, Hayes led the Rangers with 507 defensive-zone face-offs (Mika Zibanejad was second with 420) and started 57.28 percent of his 5-on-5 shifts either in the defensive zone or the neutral zone. He also led forwards in total shorthanded ice time (170:22) and per game (2:15) for New York, which tied for 10th in the NHL on the penalty kill at 81.4 percent.
"When [Derek Stepan was traded to the Arizona Coyotes], it was a big motivation for me to be a good shutdown center, and I thought I did pretty well last year with that, playing against other team's top lines, playing in the [defensive] zone, starting in the [defensive] zone above 60 percent of the time," Hayes said. "That's just a confidence builder. Points and goals, that stuff is cool individually, but that's not why we play. You have to be the right player on and off the ice every day. You have to show the coaches and the organization that you're a leader."
Hayes will enter this season with a pre-existing relationship with Quinn and his coaching staff, which he said will make the transition from former Rangers coach Alain Vigneault, the only coach he has had in his NHL career, easier.
Hayes and his family are close with Quinn, whom they have known for years, and Rangers assistant Greg Brown was an assistant at Boston College when Hayes played there from 2010-14.
"I'm not really too worried about scoring 25 or 30 goals," Hayes said. "I would like to, but it's not really a priority for me. It's showing up to the rink every day and showing the young guys what it takes to be a pro. I've had these talks with [Gorton] and [Quinn]. I think it'll all come together."