It is unclear if the Packers considered an offer for Cobb.
Cobb is a free agent this season after catching 38 passes for 383 yards and two touchdowns in nine games last season as he dealt with a hamstring issue.
Cobb, 28, had his best season in 2014 when he earned his only Pro Bowl honor with 91 catches for 1,287 yards and 12 touchdowns.
The Patriots are in the market for receivers, with Julian Edelman the only player at the position under contract for 2019 among the team’s receivers who finished last season on the active roster. Chris Hogan, Phillip Dorsett and Cordarrelle Patterson all are scheduled to become free agents.