The move was first reported by ESPN.
The former first-round pick, who has weathered arrests, a premature retirement and a financial-only suspension to start the 2015 season, played well above expectations in Dallas last season during his 13 games.
Now, he may just be in line to add some pop to Belichick's defense.
Per Rapoport, McClain is still in negotiations with the Cowboys, though a final price tag on his deal will be nowhere near what it would have been during the middle of the season last year.
Either way, the signing will be a value for a team that can secure one of the 10-best inside linebackers from a year ago at a cost nowhere near the talent level.
For McClain, his next stop will be interesting. Above all else, he's proven that the talent is there. Under Belichick, the accountability and regiment are unlike any other stop in the NFL. Could it be the right place to rehabilitate his image and sign that long-term deal?