FOXBOROUGH - Sean Payton and Bill Belichick, the two men trying to figure out how to beat each other Monday night, have never faced one another as NFL head coaches. But they have crossed paths and developed a mutual respect.

At the 2007 Pro Bowl, Belichick and Payton served as coaches, an experience both recalled fondly Wednesday. They shared a connection, both serving as assistants under Bill Parcells. They also shared proximity at the hotel the NFL used.

Payton recalled his family staying in rooms 303 and 304. Belichick had rooms 203 and 204. “My biggest concern was my little kids jumping off the beds in the morning at about 6:30 and bugging him below us,’’ Payton said.

The problem never surfaced, and Belichick and Payton struck a relationship. They fished together, talked football, and enjoyed one another’s company.

“It was a great opportunity for us,’’ Payton said. “For me, as a young coach after my first year, there might just be three or four different scheduling questions or things that you might want to get a better grasp on. He’s a guy that I have a ton of respect for and I really enjoyed the time we had a chance to spend just that week.’’

“I got to know him well and we spent a lot of time together,’’ Belichick said. “I think he’s a really sincere guy that comes from the heart. There’s not a lot of fluff and B.S. on top of it. He’s really down to earth, humble, sincere, and a man that I really respect. I respected what they did in that season. I respect what they do now. We had a chance to spend a whole day out there on a fishing trip and it was a lot of fun. It was relaxing, it was very insightful.’’

On game day, the NFL arranged six buses from the hotel to the Hula Bowl, three each for the AFC and the NFC. The NFC bus Payton rode on broke down 7 miles from the stadium. The AFC bus carrying Belichick pulled over to assist the damaged bus, which was unable to continue.

The players and coaches on the NFC bus piled onto the AFC bus, and Payton found himself sitting next to Belichick. He looked behind him and his 6-year-old son, Connor, was sitting between LaDainian Tomlinson and Drew Brees.

“And he had no idea,’’ Payton said. “But it was a good experience, one that I’ll always remember.’’

“It meant a lot,’’ rookie safety Patrick Chung said. “It’s not often he comes in and talks to us. When he does, guys listen. I looked around and everyone was focused in on him. When he comes around, everybody listens.’’

The players appreciated Kraft’s appearance.

“I feel like he really does relate to the players a lot,’’ cornerback Jonathan Wilhite said. “He’s always in the locker room, talking, conversing with the players. I didn’t think you’d get that out of a lot of owners. He’s a friendly guy. He cares about winning, and I think he really cares about the football team.

“It motivates you. You know you’ve got a higher power that believes in you, who really cares about you and this football team. It means a lot.’’

He nearly played his first game since Week 6, when he left the victory over the Titans. This week, he’s feeling better.

“It’s only been a couple days, but I think so,’’ Morris said. “Just take it as it comes, and I’ll know [if I can play] as the week goes.’’

Morris said the magnitude of Monday night’s showdown against the Saints will not provide any more motivation than usual.

“I think all the side stuff is from outside,’’ Morris said.

“It’s just as important as any week.’’

Adam Kilgore can be reached at akilgore@globe.com