Newton, 31, was forced to leave the field after undergoing foot surgery in 2019, and then was cut by the team at the end of the season.
He won the 2010 Heisman Trophy for Auburn and was selected as the No. 1 overall pick at the 2011 NFL Draft.
In 2015, Newton won the NFL MVP award for leading the Carolina Panthers to the Santa Clara Super Bowl XL.
CNN has contacted Patriots and Newton to comment.