On Monday, Belichick echoed Brady's remarks while noting that any relationship evolves over 19 years.
"We still do basically the same things we've done for quite a period of time now. I don't see that changing," Belichick said on WEEI. "I have a good relationship with Tom. I have a lot of respect for Tom. We've won a lot of games together and I hope we can win some more together. I know he feels the same way."
The relationship between Brady and Belichick became a topic of heightened interest late last season when ESPN reported on the friction between the star quarterback and the longtime coach, stemming from Brady's ties to trainer Alex Guerrero.
The Patriots added $5 million in incentives to Brady's contract last week, while converting $10 million of his base salary to a signing bonus. In doing so, it kept Brady's salary-cap charge at $22 million for the 2018 season, while upping it to $27 million in 2019, which is the last year of the contract.
Asked if he was happy with the change, Brady said on WEEI, "I've never talked about my contract and that's never been the top priority for me. I love being here, this community, this organization. I love winning and I love that my family has had a home for a long time. Those have been my priorities as long as I've been in this game."
As for his future, he said, "I certainly expect to be here next year and hopefully beyond. I have goals to play for a long time. I still love doing it. I still want to do it. But I'm also focused on what I need to do this year. It's a tough challenge, and it's a great challenge. I've loved it for a long time and I still want to get out there and be the best I can be for our team."
Asked if he plans to play in 2020, Brady said on WEEI, "I hope so. You have to have goals for the long-term and short-term, and I have long-term goals that I set for myself that I would love to be able to accomplish. I know it's not easy. Any one game could be the end, at the end of the day, I think that's what you realize as a player.
"I've played with a lot of guys, and sure you have goals, but at the same time it's a physical sport, a demolition derby. You never know when you're going to come out of it. I'm always trying to take good care of myself, I'm always trying to put myself in a position where I can execute my job and take the hits and perform well. I think I've got a really great routine and I'd like to continue to show that I can do it."
Brady, who had been managing a sore back, didn't play in Thursday's preseason opener against the Washington Redskins. His workload in practice has picked up in recent days.
Asked if he plans on playing in Thursday's preseason game against the Philadelphia Eagles, he said, "absolutely."