Buccaneers general manager Jason Licht said on The Rich Eisen Show that a new deal for the 43-year-old is "a possibility."
Even before Tampa's 31-9 victory over the Kansas City Chiefs on Feb. 7, speculation about Brady and the Bucs looking at a contract extension had begun.
Head coach Bruce Arians told reporters leading up to the Super Bowl that he "wouldn't be surprised" if the Buccaneers talked about a new deal with the 14-time Pro Bowler this offseason.
The quarterback signed a two-year, fully guaranteed $50 million contract with Tampa Bay last March. There were questions about how well he would be able to perform in a new system after 20 years with the Patriots.
Any concerns about Brady's age were quickly squashed, as he looked perfectly comfortable in Arians' offense that emphasizes downfield passing. He had his most passing yards (4,633) and completions (402) since 2015. His 40 touchdown passes were his second-most in a single season (50 in 2007).
The Buccaneers went 11-5 in the regular season and made the postseason for the first time since 2007.
Brady threw for 1,061 yards with 10 touchdowns and three interceptions in Tampa's four playoff wins. He won his record seventh Super Bowl and was named Super Bowl MVP for a record fifth time.