Jeff Howe of the Boston Herald reported Thursday that the two sides are in "very early talks" regarding a new deal.
Brady, 39, has three years remaining on his current contract. He is set to make $1 million in base salary in 2017, but that number rises to $14 million in 2018 and 2019, per Spotrac.
The Patriots will understandably be more inclined to restructure the latter two seasons of the deal. Brady counts for $22 million against the cap in 2018 and 2019, compared to just $14 million in 2017. A new deal might lower the base salaries in those final two years while adding some length and guaranteed money to the contract to keep his cap hold low.
What's abundantly clear is that Brady has no plans to retire now or anytime soon. The Patriots quarterback has long insisted he would play well into his 40s, telling a group of reporters in October 2015 that he wanted to go for another decade.
"If it was up to my wife, she'd have me retire today. She told me that last night. I said, 'Too bad, babe,'" Brady said on the Monday after Super Bowl LI on SiriusXM NFL Radio.
Brady is coming off perhaps the crowning achievement of his career, a Super Bowl-record 25-point comeback over the Atlanta Falcons. The Patriots trailed 28-3 with under 18 minutes to play and then scored the game's final 31 points in a 34-28 overtime thriller.
Brady threw for a Super Bowl-record 466 yards while also setting marks for completions (43) and pass attempts (62). His five Super Bowl championships are tied with Charles Haley for the most by a player, and he broke the all-time mark for Super Bowl MVPs with four.
"I don't think anything about a personal legacy," Brady said, per Kevin Van Valkenburg of ESPN.com. "I mean, those words would never come out of my mouth unless I just repeated them. Those things have never been important to me."
The only real issue here is whether Brady can continue bucking history and stay effective into his 40s. Brady, who turns 40 on August 3, already became the second-oldest quarterback to win a Super Bowl, just months behind Peyton Manning.
Brett Favre and Warren Moon are the only quarterbacks in NFL history to make a Pro Bowl in their age-40 season or later. Favre, Moon and Vinny Testaverde are the only three who have so much as thrown for 3,000 yards after age 40, per Pro Football Reference.
With Jimmy Garoppolo waiting in the wings, there might have been some rumblings about moving on had Brady faltered in the postseason. Now, after perhaps the apex of his career, it's impossible to imagine when or if the Patriots could move on.