Mathis is the a top three offensive guard in the league and he was slated to earn $5.5 million this upcoming season. According to Eagles head coach Chip Kelly, Mathis has been on the trade block for two years, so it's evident that Mathis hasn't bought into Kelly's system, even though the lineman has been producing at an extremely high level. Mathis is 33 years old so his potential as a trade option was extremely limited.
The Patriots have also invested two fourth round picks in guards Tre Jackson and Shaq Mason, which implies that New England has their future at the position set. However, New England is far from set in stone for the upcoming year.
The Patriots have the rookie Jackson and the veteran Ryan Wendell prepared as the starting guards in 2015. As a rookie, Jackson has little claim to the starting position, while Wendell started out of necessity- he's the Patriots fourth choice to act as a starting guard in 2014. Even though Wendell played well, he's in the final year of his contract and it's a common thought that the Patriots wish to upgrade at the role.
Mathis is in the twilight of his career and it would make sense that he would like to play for a competitor, and no team is more competitive than New England. Mathis would step in as a starting left guard, similar to how veteran Brian Waters put in a Pro Bowl year at right guard in the Patriots 2011 season.
The addition of Mathis would replace the free agent Dan Connolly and would allow Jackson and Wendell to have open competition for the starting right guard position, while Mason would continue to develop as a project. The Patriots are in a position where they'll likely have to rely on a rookie starting in Week 1 on their offensive line, which is less than ideal. An addition of Mathis would both strengthen the starting line-up and provide the Patriots rookies with a star interior lineman to follow as they grow at the NFL level.