But likely only as a backup option.
Smith is recovering from a torn ACL and while he has visited multiple teams, the fact that he remains unsigned could be an indication teams will wait for a clean bill of health before offering Smith a contract.
A prolific college quarterback at West Virginia, Smith has not started and finished a game since 2014. He was expected to start in 2015 for the Jets despite a coaching change, but Todd Bowles never re-opened the door for Smith as he was decked in a locker room spat with IK Enemkpali, a teammate and linebacker who alleged Smith owed him $600.
When he finally got back on the field last season as the Week 7 starter, Smith left the game with a torn knee ligament and landed on injured reserve.
In Cleveland, Smith could compete with a roster full of unproven passers, including Cody Kessler.
The Jets are showing interest in former Bears quarterback Jay Cutler and have studied the top quarterbacks in the 2017 draft. Christian Hackenberg and Bryce Petty are expected to be in the competition at quarterback with the Jets but neither nailed down a spot in 2016.
Smith has 36 interceptions in 33 career games.
The Giants and Chargers are looking for backups - to Eli Manning and Philip Rivers, top-4 draft picks in the 2004 draft - to longtime starters but Smith said in February that his expectations are to be in the mix for the starting job.