Cousins went 1-4 in his five starts this season, including a four-interception performance in a 45-14 loss at home against the New York Giants in Week 4.
Griffin III started the last three games of the season after McCoy was placed on injured reserve with a neck injury.
Cousins, 26, is scheduled to earn a base salary of $660,000 next season before hitting the free agent market in 2016. In three seasons, Cousins has 3,030 passing yards with 18 touchdowns and 19 interceptions.
- Scooby Axson