Citing an unnamed NFL sources, the magazine said Brady -- who has guided the Patriots to three Super Bowl titles -- has signed a deal worth $27 million, which will keep him with the team until 2017 when he will be 40 years old.
SI reported the extension will pay Brady an immediate $3 million signing bonus as well as salaries of $7 million in 2015, $8 million in 2016 and $9 million in 2017.
If true, the relatively conservative contract will allow the Patriots more room under the NFL's flat salary cap restrictions, including a total of $15 million over the next two seasons, thus enabling them to more easily assemble a talented team around him.
Over his 13-year career, Brady has been named the Super Bowl most valuable player and league MVP twice and has been selected to the Pro Bowl eight times.
In 2012 he led the Patriots to their fourth straight AFC East title and guided an offense that broke the NFL record for most first downs in a season with 444.
The Pats lost to the Baltimore Ravens in the AFC championship game.