The quarterback missed the final six games of the 2012 season for the Jags with an elbow injury.
General manager David Caldwell told the Florida Times-Union: "That was his second year. What were they saying about other quarterbacks after their second year?
"We're looking for improvement. We need to build around him. We'll upgrade whenever we can upgrade."
Gabbert threw nine touchdowns and six interceptions in his 10 games in 2012, but recorded just one win.