The three-time Super Bowl winning quarterback has two seasons left on his current contract with the franchise, and will be 38 when it expires, having previously said that he wants to play until he is at least 40.
The Patriots owner told CSN New England: "I think he had a remarkable year this year and I think we look at each year as it happens. I'd love him to be here as long as he's productive and feels he wants to play.
"That's his choice [to move to another team] but I would surely never like to see that happen. I think what he's done for this franchise, but once again, everything is a dual decision.
"But I think, somehow I feel he'll know when it's not right for him and I believe he loves being a Patriot and we sure love having him be part of our organisation."
Brady led the Patriots to the AFC East title for the 10th time in his career during the 2012 season, but missed out on his sixth Super Bowl appearance following defeat to the Baltimore Ravens in the AFC Championship game.