The 36-year-old was a free agent after being released by the Washington Football Team earlier this offseason. He said he visited Jacksonville to potentially reunite with head coach Urban Meyer, who coached the quarterback in college at Utah.
Tom Pelissero of NFL Network reported "multiple teams" wanted to sign Smith.
The Jaguars hold the No. 1 pick and are widely expected to select Clemson quarterback Trevor Lawrence. The team also still has Gardner Minshew, who has proved to be a serviceable player under center.
Smith could have still helped the young team with his experience and consistency on the field.
While the 2020 Comeback Player of the Year didn't put up big numbers with Washington last season—197.8 passing yards per game with six touchdowns and eight interceptions—the squad went 5-1 with Smith as a starter. The NFC East winners went just 2-8 with Dwayne Haskins and Kyle Allen starting the game.
After being released, Smith was searching for a new team, and Dan Graziano and Jeremy Fowler of ESPN reported the quarterback "would prefer to go to a place where he could compete for a starting job."
Even if he could have started Week 1 in Jacksonville, it would likely have only been a matter of time before Lawrence or another young quarterback took over the role.