Levitre had his salary slashed $2.5 million, reducing his salary cap number from $8.3 million to $5.6 million, the Atlanta Journal Constitution reported, citing NFL Players Association documents.
The cut in pay lowered Levitre's base salary to $3.5 million, which is fully guaranteed for next season. Falcons general manager Thomas Dimitroff told the newspaper at the NFL Combine that Levitre would be back with the team.
Levitre started all 13 games in which he played last season. The 31-year-old Levitre had started all 16 games in his previous eight seasons with Buffalo, Tennessee and Atlanta.
Meanwhile, the NFL Network's Ian Rapoport reported that Brooks agreed to restructure his contract. Reed had been scheduled to earn $4.5 million.
Reed, 31, appeared in 16 games, making 14 starts, last season and registered 4.0 sacks -- his highest total since racking up 6.0 sacks as a rookie in 2011 with Houston.