According to his agent, Drew Rosenhaus, the deal is worth up to $3.75 million.
Gilbert suffered a torn ACL just before Week 1 and missed the 2019 season after he was traded from the Pittsburgh Steelers to the Cardinals last March.
He appeared in 88 games (87 starts) over eight seasons with the Steelers after they drafted him in the second round in 2011.
According to NFL Next Gen Stats, in a limited sample (5 starts, 194 pass blocks), Gilbert recorded a pass block win rate of 87% -- the best of all Steelers offensive linemen in 2018.
The 32-year-old was entering the final season of a five-year extension when he got hurt.
ESPN's Adam Schefter and Josh Weinfuss contributed to this report.