Both players have undergone surgery since last season.
Conley had offseason ankle surgery, while Cole is recovering from a torn ACL suffered in his right knee in 2019.
The Texans project Conley to be their starting quarterback opposite Bradley Roby, who signed a three-year deal for $36 million this offseason to remain with the team.
Conley, however, did not have his fifth-year option picked up by the Texans, despite them trading a third-round pick for him just before their Week 8 matchup against his former team, the Oakland Raiders.
Cole has been a team captain and the Texans' primary backup to Benardrick McKinney and Zach Cunningham.