Grossman has not played in an NFL game since 2011.
Grossman, 35, was attempting a comeback after failing to make an NFL team in 2014. He signed a one-year deal with the Falcons in late-August.
Grossman spent last summer in training camp with the Browns, but was cut before the season began. He was then offered a contract by the Browns in late-December after quarterbacks Brian Hoyer and Johnny Manziel went down with injuries, but declined the offer to spend the holidays with his family.
- Christopher Chavez