Brinkley has to pass a physical before it becomes official.
The Cowboys have lost Justin Durant (Atlanta Falcons) and Bruce Carter (Tampa Bay Buccaneers) in free agency, Brinkley would become the second free agent to join the roster with Keith Rivers, who played for the Buffalo Bills last season.
Brinkley, who turns 30 in July, started 11 of 16 games for the Minnesota Vikings in 2014 and had 54 tackles, one sack and one forced fumble. After a three-year run with the Vikings from 2009-12, he played for the Arizona Cardinals in 2012.
Brinkley is a middle linebacker and two-down player, which could allow the Cowboys to use Sean Lee at the weak-side linebacker position as he returns from a torn ACL. The Cowboys have considered using Lee, who played middle linebacker in 2013, on the weak side in case Rolando McClain returned in 2015.
McClain, who the coaches credited with 108 tackles in 12 games in 2014, is a free agent and the team has had discussions about him returning. He is facing a four-game fine for violating the NFL’s substance-abuse policy, according to sources.