Brady has one year remaining on his contract but both sides have expressed interest in prolonging the relationship. The 43-year-old quarterback said he'd "definitely" consider the possibility of playing past the age of 45, and general manager Jason Licht also expressed interest in extending Brady.
The extension would give Tampa Bay salary-cap relief for 2021 and room to retain a championship-caliber roster, Schefter adds.
Brady carries a salary-cap hit of $28.4 million this year, but a new contract would likely decrease that figure.
The Buccaneers signed the former New England Patriots signal-caller to a two-year, $50-million deal last offseason.
Brady threw for 40 touchdowns and 4,633 yards in his first season with Tampa Bay, leading the team to a Super Bowl championship.