The deal is worth up to $7.5 million, according to NFL Network's Ian Rapoport.
The 31-year-old appeared in just two games for the Carolina Panthers in 2019 after suffering an early Lisfranc fracture. His rehab took longer than expected, and he finished the year on the injured reserve.
In March, the Panthers released the 2015 MVP after nine seasons.
Newton, the first overall pick in 2011, led Carolina to a 15-1 record in 2015, tossing for 3,837 yards and 35 touchdowns while also running for 636 yards and 10 scores. He was named Offensive Rookie of the Year in 2011, and Offensive Player of the Year four years later.
The three-time Pro Bowler made 16 starts with the Panthers dating back to 2018. He posted a 6-10 record and completed 66.1% of his pass attempts for 3,967 yards and 24 touchdowns against 14 interceptions. He also added four scores on the ground.
Newton's future with the Panthers came into question when the team decided to rebuild. Carolina named Matt Rhule its new head coach this offseason, and the team signed quarterback Teddy Bridgewater to a three-year deal.
The Patriots, meanwhile, lost quarterback Tom Brady during the early days of free agency. Second-year signal-caller Jarrett Stidham and veteran Brian Hoyer are the other options on New England's quarterback depth chart.
The Patriots are expected to make roster moves before officially landing Newton due to their tight salary-cap situation.