Signing Cobb would keep the Cowboys from "needing" to take a wide receiver early in the draft, and would allow them to easily shed Allen Hurns if a receiving weapon did fall to them at 58th overall. He missed seven games last season to a concussion and hamstring injury.
Six-time Pro Bowl linebacker Clay Matthews, the Packers' all-time sacks leader, has agreed to a two-year contract with the Los Angeles Rams.
The 28-year-old has tallied 41 career receiving scores.
Despite Cobb's limited production, quarterback Aaron Rodgers stated the receiver's importance to the Packers' offense late in the season when he said: "When Randall's healthy, I think our offense has been different because we have a true slot guy who can make plays in the slot consistently".
"I've enjoyed being here".
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Cobb finishes his run in Green Bay as one of just five players in franchise history to register more than 60 receptions in four consecutive seasons (2014-17).
Some of Beasley's production on underneath and over-the-middle routes could also be replaced by tight end Jason Witten, who returned to the Cowboys after spending last season as an analyst on ESPN's "Monday Night Football".
Without an abundance of salary cap space to work with, the Cowboys have been relatively quiet in free agency, but the team was reported Tuesday to have hosted a couple of the bigger names available: pass-rusher Robert Quinn and safety Eric Berry.
The Cowboys and Miami Dolphins have had discussions regarding a trade for Quinn, according to multiple sources.
A star Packers player is reportedly going to the Cowboys.
So, while Cobb unfortunately never captured a ring with the Packers, he does leave the team still holding a distinction that no other player in National Football League history can claim.