The Packers are seeking a veteran cornerback to compete or replace Ahmad Carroll, who has struggled the past two seasons.
Woodson recently met with the Buccaneers but also left without a contract. He likely is seeking a deal with an average salary of $4 million to $5 million per season.
Woodson, 29, was the fourth player chosen overall in the 1998 NFL Draft. He was Oakland's franchise player the last two seasons, but the Raiders reportedly have no interest in re-signing him.
Woodson missed the final 10 games of last season with a broken leg. He has missed 21 of the last 48 games over the past four seasons due to injuries.