The Patriots are slated to sign Gibson, Ian Rapoport of NFL Network reports.
Gibson finished 2023 with 65 carries for 265 yards and a touchdown and 48 catches for 389 yards and two touchdowns on 59 targets.
Gibson recorded four carries for 19 yards and gathered in two of four targets for 17 yards during Sunday's 27-10 loss to the 49ers.
Gibson carried the ball nine times for 30 yards and a touchdown and caught one of two targets for two yards in Sunday's 30-28 loss to the Jets.
Gibson took four carries for 15 yards and caught each of his five targets for 20 yards in a 28-20 loss to the Rams on Sunday.
Gibson and Chris Rodriguez will lead Washington's backfield Sunday against the Rams with Brian Robinson (hamstring) ruled out, Zach Selby of the team's official site reports.
Gibson rushed 10 times for 35 yards and brought in four of five targets for 37 yards in the Commanders' 45-15 loss to the Dolphins on Sunday. He also fumbled once but recovered.
Gibson took six carries for 21 yards and caught three of four targets for 16 yards in a 45-10 loss to Dallas on Thursday.
Gibson (toe) is listed as active Thursday in Dallas.
Gibson is listed as questionable for Thursday's matchup with Dallas and may be a game-time decision, Ian Rapoport of NFL Network reports.