New England brought Reece in for a workout last week but did not sign him to a contract following the session.
Reece just finished serving his four-game suspension, which dated back to last year, when he was cut loose by the Raiders last week.
Reece, 31, was in the final year of his four-year, $14.423 contract that included $7.2 million guaranteed and set to make a base salary of $2.6 million for the 2016 season when Oakland released him in a move that freed up $2,191,176 in available cap space.
In 2015, Reece appeared in 15 games for the Raiders and ran for 36 yards on 10 carries to go along with 30 receptions for 269 yards receiving and three touchdowns.
We’ll have more regarding Reece possibly signing with the Patriots as the news is available.