This comes shortly after the news that the Rams have released RB Todd Gurley.
Matthews, 33, is a former first-round pick of the Packers back in 2009. He played out the final year of his six-year, $69.73 million contract and made a base salary of $10.4 million for the 2018 season.
The Rams signed Matthews to a two-year contract worth up to $16.75 million last year.
According to OverTheCap.com, releasing Matthews will free up $3,750,000 of available cap space while creating $2 million in dead money.
In 2019, Matthews appeared in 13 games for the Rams and recorded 37 tackles, eight sacks, two forced fumbles and three pass defenses.