Monroe will find a role in an offense that is ranked 28th in rushing offense this season with an average of 64 yards per game.
NFL sources told the Baltimore Sun Monroe would be in Baltimore Wednesday to take a physical. The trade will be finalized if he passes.
Monroe was taken by Jacksonville with the eighth overall draft pick in 2009 and has started 62 games in his career. The Jaguars are 0-4 this season and were expected to move rookie Luke Joeckel, the second overall pick this year, into the starting left tackle slot, and stockpile the unspecified picks it receives from Baltimore.