Dobbs, 27, entered the league with the Pittsburgh Steelers in the fourth round of the 2017 draft at No. 135 overall. The Tennessee product and Reese’s Senior Bowl participant has also been a member of the Jacksonville Jaguars.
Jacksonville acquired Dobbs in exchange for a fifth-round selection to begin 2019. He was claimed off waivers by Pittsburgh the following September at the 53-man roster deadline.
Through six career games in the regular season, Dobbs has gone 10-of-17 passing for 45 yards with one interception. He has added six rushing attempts for 31 yards.
Dobbs, listed at 6-foot-3, 216 pounds, finished his Volunteers tenure with a 23-12 record as a starter. He set all-time program records for rushing yards and rushing touchdowns at the position while ranking fifth in passing yards and third in total offense.
New England’s quarterback depth chart stands with Mac Jones, Jarrett Stidham and Brian Hoyer, who re-signed as free agency opened last week, under contract.
The organization also had running back Leonard Fournette, offensive lineman Ryan Bates and cornerback Malcolm Butler in for visits on Monday.