Woodley, 26, who just finished his third season with Pittsburgh, had 50 tackles, 10 sacks and two interceptions last season, helping the Steelers to the AFC championship. The former second-round pick out of Michigan has 39 sacks and seven forced fumbles for his career.
He made $550,000 last season, the final year of his rookie contract. But, because of the tag and his position, Woodley stands to make more than $10 million next season, if the Steelers don't sign him to a long-term contract.
In the Steelers' three-game playoff run, Woodley had 10 tackles and three sacks.
A member of the 2010 AFC Pro Bowl squad, Woodley is the only player in NFL history to post at least one sack in six consecutive postseason games. He has 11 sacks total in seven postseason contests, including an NFL record two in each of his first four playoff outings.