The Browns could use some offensive line help, so this could be someone to keep an eye on in the coming days in case Cleveland makes a move.
Bernadeau previously worked out for the Giants but did not receive an offer from the team.
Bernadeau, 30, is a former seventh-round pick of the Panthers back in 2009. He spent three years in Carolina before signing on with the Cowboys back in 2012.
Jacksonville elected to sign him to a two-year contract this past March before later releasing him as they cut their roster down to 53 players.
In 2015, Bernadeau was active for all 16 games for the Cowboys , but played a total of 96 snaps for them, according to Pro Football Focus.