The 27-year-old started the 2012 campaign as backup to Blaine Gabbert, but he played in 10 games after his teammate was injured.
Henne told the Florida Times-Union: "Sure, this is a great opportunity. You've seen all the moves with quarterbacks going all over the league and this is one of those opportunities.
"There's a starting job open and let the best man win. I'm just going to give it my all. I'm still young. I'm only 27 years old in my sixth season.
"Aaron Rodgers started when he was five years in. I'm only a year behind right now. I'm a competitor. I'm going to compete."
Henne joined the Jaguars in 2012, having spent the first four years of his NFL career with the Miami Dolphins.